%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL095-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 3.80s 1.07s
% Output : Proof 266.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL095-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n018.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 15:23:53 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.80/1.07 Command-line arguments: --no-flatten-goal
% 3.80/1.07
% 3.80/1.07 % SZS status Unsatisfiable
% 3.80/1.07
% 209.14/30.42 % SZS output start Proof
% 209.14/30.42 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 209.14/30.42 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.
% 211.50/30.77 Axiom 3 (ic_JLukasiewicz_5): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))) = true.
% 211.50/30.77
% 211.50/30.77 Goal 1 (prove_ic_5): is_a_theorem(implies(a, implies(implies(a, b), b))) = true.
% 211.50/30.77 Proof:
% 211.50/30.77 is_a_theorem(implies(a, implies(implies(a, b), b)))
% 211.50/30.77 = { by axiom 1 (ifeq_axiom) R->L }
% 211.50/30.77 ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.77 = { by axiom 2 (condensed_detachment) R->L }
% 211.50/30.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.77 = { by axiom 1 (ifeq_axiom) R->L }
% 211.50/30.77 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.78 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.50/30.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.78 = { by axiom 1 (ifeq_axiom) R->L }
% 211.50/30.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.78 = { by axiom 2 (condensed_detachment) R->L }
% 211.50/30.78 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.78 = { by axiom 1 (ifeq_axiom) R->L }
% 211.50/30.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.79 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.50/30.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(implies(Z, W), implies(W, Y))), implies(W, X)), implies(implies(X, Y), implies(implies(U2, implies(T2, W)), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.79 = { by axiom 1 (ifeq_axiom) R->L }
% 211.50/30.79 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(implies(Z, W), implies(W, Y))), implies(W, X)), implies(implies(X, Y), implies(implies(U2, implies(T2, W)), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.50/30.80 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.80 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(implies(Z, W), implies(W, Y))), implies(W, X)), implies(implies(X, Y), implies(implies(U2, implies(T2, W)), implies(W, Y)))), implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(implies(Z, W), implies(W, Y))), implies(W, X)), implies(implies(X, Y), implies(implies(U2, implies(T2, W)), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.80 = { by axiom 2 (condensed_detachment) }
% 211.96/30.80 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.80 = { by axiom 1 (ifeq_axiom) }
% 211.96/30.81 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.81 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.81 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.81 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.81 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, Y), implies(T2, Z)), implies(implies(Z, W), implies(U2, implies(T2, W))))), true, is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.81 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.81 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, Y), implies(T2, Z)), implies(implies(Z, W), implies(U2, implies(T2, W))))), true, is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.82 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.82 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, Y), implies(T2, Z)), implies(implies(Z, W), implies(U2, implies(T2, W)))), implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(W, Y), implies(T2, Z)), implies(implies(Z, W), implies(U2, implies(T2, W))))), true, is_a_theorem(implies(implies(implies(U2, implies(T2, W)), implies(W, Y)), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.82 = { by axiom 2 (condensed_detachment) }
% 211.96/30.82 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.82 = { by axiom 1 (ifeq_axiom) }
% 211.96/30.82 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2)))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, Y2), implies(Z2, W2)), implies(implies(W2, X2), implies(V2, implies(Z2, X2))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.82 = { by axiom 2 (condensed_detachment) }
% 211.96/30.82 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.83 = { by axiom 1 (ifeq_axiom) }
% 211.96/30.83 ifeq(ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.83 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.83 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.83 = { by axiom 2 (condensed_detachment) R->L }
% 211.96/30.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.83 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.83 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.86 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.86 = { by axiom 2 (condensed_detachment) R->L }
% 211.96/30.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.87 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.87 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))), implies(Z3, S2)), implies(implies(S2, X3), implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.88 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))), implies(Z3, S2)), implies(implies(S2, X3), implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.88 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 211.96/30.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))), implies(Z3, S2)), implies(implies(S2, X3), implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)))), implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))))), true, ifeq(is_a_theorem(implies(implies(implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))), implies(Z3, S2)), implies(implies(S2, X3), implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.89 = { by axiom 2 (condensed_detachment) }
% 211.96/30.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.89 = { by axiom 1 (ifeq_axiom) }
% 211.96/30.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 211.96/30.90 = { by axiom 1 (ifeq_axiom) R->L }
% 211.96/30.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.90 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 212.65/30.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(Y4, Y3)), implies(implies(Y3, Z3), implies(X4, implies(Y4, Z3))))), true, is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.90 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(Y4, Y3)), implies(implies(Y3, Z3), implies(X4, implies(Y4, Z3))))), true, is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.90 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 212.65/30.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, X3), implies(Y4, Y3)), implies(implies(Y3, Z3), implies(X4, implies(Y4, Z3)))), implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(Y4, Y3)), implies(implies(Y3, Z3), implies(X4, implies(Y4, Z3))))), true, is_a_theorem(implies(implies(implies(X4, implies(Y4, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.91 = { by axiom 2 (condensed_detachment) }
% 212.65/30.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.91 = { by axiom 1 (ifeq_axiom) }
% 212.65/30.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(U3, T3)), implies(implies(T3, W3), implies(S3, implies(U3, W3))))), true, is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.91 = { by axiom 2 (condensed_detachment) }
% 212.65/30.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, ifeq(true, true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.91 = { by axiom 1 (ifeq_axiom) }
% 212.65/30.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.92 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.92 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.92 = { by axiom 2 (condensed_detachment) R->L }
% 212.65/30.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), true, ifeq(is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.92 = { by axiom 3 (ic_JLukasiewicz_5) }
% 212.65/30.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.92 = { by axiom 1 (ifeq_axiom) }
% 212.65/30.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.93 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.93 = { by axiom 2 (condensed_detachment) R->L }
% 212.65/30.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.94 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.95 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 212.65/30.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.95 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.96 = { by axiom 2 (condensed_detachment) R->L }
% 212.65/30.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))))), true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.97 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.98 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 212.65/30.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W4, implies(implies(V4, U4), implies(U4, W4))), implies(U4, Z4)), implies(implies(Z4, W4), implies(implies(S5, implies(X6, U4)), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.99 = { by axiom 1 (ifeq_axiom) R->L }
% 212.65/30.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W4, implies(implies(V4, U4), implies(U4, W4))), implies(U4, Z4)), implies(implies(Z4, W4), implies(implies(S5, implies(X6, U4)), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 212.65/30.99 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 213.38/31.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W4, implies(implies(V4, U4), implies(U4, W4))), implies(U4, Z4)), implies(implies(Z4, W4), implies(implies(S5, implies(X6, U4)), implies(U4, W4)))), implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))))), true, ifeq(is_a_theorem(implies(implies(implies(W4, implies(implies(V4, U4), implies(U4, W4))), implies(U4, Z4)), implies(implies(Z4, W4), implies(implies(S5, implies(X6, U4)), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.00 = { by axiom 2 (condensed_detachment) }
% 213.38/31.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.01 = { by axiom 1 (ifeq_axiom) }
% 213.38/31.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.02 = { by axiom 1 (ifeq_axiom) R->L }
% 213.38/31.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.03 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 213.38/31.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U4, W4), implies(X6, V4)), implies(implies(V4, U4), implies(S5, implies(X6, U4))))), true, is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.03 = { by axiom 1 (ifeq_axiom) R->L }
% 213.38/31.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U4, W4), implies(X6, V4)), implies(implies(V4, U4), implies(S5, implies(X6, U4))))), true, is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.04 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 213.38/31.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U4, W4), implies(X6, V4)), implies(implies(V4, U4), implies(S5, implies(X6, U4)))), implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true, ifeq(is_a_theorem(implies(implies(implies(U4, W4), implies(X6, V4)), implies(implies(V4, U4), implies(S5, implies(X6, U4))))), true, is_a_theorem(implies(implies(implies(S5, implies(X6, U4)), implies(U4, W4)), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.05 = { by axiom 2 (condensed_detachment) }
% 213.38/31.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.05 = { by axiom 1 (ifeq_axiom) }
% 213.38/31.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5))))), true, is_a_theorem(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.06 = { by axiom 2 (condensed_detachment) }
% 213.38/31.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.06 = { by axiom 1 (ifeq_axiom) }
% 213.38/31.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.07 = { by axiom 1 (ifeq_axiom) R->L }
% 213.38/31.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.08 = { by axiom 2 (condensed_detachment) R->L }
% 213.38/31.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.09 = { by axiom 3 (ic_JLukasiewicz_5) }
% 213.38/31.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 213.38/31.10 = { by axiom 1 (ifeq_axiom) }
% 214.07/31.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.11 = { by axiom 1 (ifeq_axiom) R->L }
% 214.07/31.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.12 = { by axiom 2 (condensed_detachment) R->L }
% 214.07/31.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.13 = { by axiom 1 (ifeq_axiom) R->L }
% 214.07/31.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.14 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 214.07/31.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.16 = { by axiom 1 (ifeq_axiom) R->L }
% 214.07/31.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.18 = { by axiom 2 (condensed_detachment) R->L }
% 214.07/31.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))))), true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.07/31.19 = { by axiom 1 (ifeq_axiom) R->L }
% 214.78/31.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.21 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 214.78/31.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W6, implies(implies(V6, U6), implies(U6, W6))), implies(U6, Z6)), implies(implies(Z6, W6), implies(implies(W7, implies(V7, U6)), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.23 = { by axiom 1 (ifeq_axiom) R->L }
% 214.78/31.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(implies(V6, U6), implies(U6, W6))), implies(U6, Z6)), implies(implies(Z6, W6), implies(implies(W7, implies(V7, U6)), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.24 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 214.78/31.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, implies(implies(V6, U6), implies(U6, W6))), implies(U6, Z6)), implies(implies(Z6, W6), implies(implies(W7, implies(V7, U6)), implies(U6, W6)))), implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))))), true, ifeq(is_a_theorem(implies(implies(implies(W6, implies(implies(V6, U6), implies(U6, W6))), implies(U6, Z6)), implies(implies(Z6, W6), implies(implies(W7, implies(V7, U6)), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.26 = { by axiom 2 (condensed_detachment) }
% 214.78/31.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.28 = { by axiom 1 (ifeq_axiom) }
% 214.78/31.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 214.78/31.29 = { by axiom 1 (ifeq_axiom) R->L }
% 215.47/31.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.31 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 215.47/31.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U6, W6), implies(V7, V6)), implies(implies(V6, U6), implies(W7, implies(V7, U6))))), true, is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.32 = { by axiom 1 (ifeq_axiom) R->L }
% 215.47/31.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U6, W6), implies(V7, V6)), implies(implies(V6, U6), implies(W7, implies(V7, U6))))), true, is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.34 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 215.47/31.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U6, W6), implies(V7, V6)), implies(implies(V6, U6), implies(W7, implies(V7, U6)))), implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true, ifeq(is_a_theorem(implies(implies(implies(U6, W6), implies(V7, V6)), implies(implies(V6, U6), implies(W7, implies(V7, U6))))), true, is_a_theorem(implies(implies(implies(W7, implies(V7, U6)), implies(U6, W6)), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.35 = { by axiom 2 (condensed_detachment) }
% 215.47/31.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.37 = { by axiom 1 (ifeq_axiom) }
% 215.47/31.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6)))), implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))))), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(implies(Y7, T6), implies(Z7, implies(X7, T6))))), true, is_a_theorem(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 215.47/31.38 = { by axiom 2 (condensed_detachment) }
% 215.47/31.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 216.17/31.40 = { by axiom 1 (ifeq_axiom) }
% 216.17/31.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 216.17/31.42 = { by axiom 1 (ifeq_axiom) R->L }
% 216.17/31.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 216.17/31.44 = { by axiom 2 (condensed_detachment) R->L }
% 216.17/31.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 216.17/31.47 = { by axiom 1 (ifeq_axiom) R->L }
% 216.17/31.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 216.89/31.51 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 216.89/31.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, 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% 216.89/31.54 = { by axiom 1 (ifeq_axiom) R->L }
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% 216.89/31.58 = { by axiom 2 (condensed_detachment) R->L }
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% 216.89/31.63 = { by axiom 1 (ifeq_axiom) R->L }
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% 217.99/31.68 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 217.99/31.72 = { by axiom 1 (ifeq_axiom) R->L }
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% 218.71/31.76 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 219.03/31.81 = { by axiom 2 (condensed_detachment) }
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% 219.03/31.85 = { by axiom 1 (ifeq_axiom) }
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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), 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% 219.03/31.89 = { by axiom 1 (ifeq_axiom) R->L }
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% 219.73/31.93 = { by axiom 2 (condensed_detachment) R->L }
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% 219.73/31.97 = { by axiom 1 (ifeq_axiom) R->L }
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% 220.41/32.01 = { by axiom 2 (condensed_detachment) R->L }
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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)), implies(U9, T8)), implies(implies(T8, S8), implies(T9, implies(U9, S8)))), implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))))), true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)), implies(U9, T8)), implies(implies(T8, S8), implies(T9, implies(U9, S8))))), true, is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), 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implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 220.41/32.05 = { by axiom 3 (ic_JLukasiewicz_5) }
% 220.41/32.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)), implies(U9, T8)), implies(implies(T8, S8), implies(T9, implies(U9, S8))))), true, is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), 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is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), 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b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 220.41/32.10 = { by axiom 1 (ifeq_axiom) }
% 221.12/32.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)), implies(U9, T8)), implies(implies(T8, S8), implies(T9, implies(U9, S8))))), true, is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true, is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), 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b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 221.12/32.15 = { by axiom 3 (ic_JLukasiewicz_5) }
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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true, is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Z9, W9)), 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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, 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% 221.84/32.21 = { by axiom 1 (ifeq_axiom) }
% 221.84/32.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true, is_a_theorem(implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), 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% 221.84/32.26 = { by axiom 1 (ifeq_axiom) R->L }
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% 222.53/32.31 = { by axiom 2 (condensed_detachment) R->L }
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implies(W8, Y8)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), 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implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 222.53/32.37 = { by axiom 3 (ic_JLukasiewicz_5) }
% 222.53/32.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))), implies(S8, implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true, is_a_theorem(implies(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, 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% 223.22/32.42 = { by axiom 1 (ifeq_axiom) }
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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), 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true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 223.22/32.47 = { by axiom 3 (ic_JLukasiewicz_5) }
% 223.22/32.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T9, implies(U9, S8)), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))))), implies(implies(implies(implies(X9, Y9), implies(Z9, W9)), implies(implies(W9, X9), implies(V9, implies(Z9, X9)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(U9, S8)), implies(S8, 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% 223.93/32.51 = { by axiom 1 (ifeq_axiom) }
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% 223.93/32.55 = { by axiom 2 (condensed_detachment) }
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% 223.93/32.58 = { by axiom 1 (ifeq_axiom) }
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b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 223.93/32.62 = { by axiom 3 (ic_JLukasiewicz_5) }
% 223.93/32.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, 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implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 225.00/32.66 = { by axiom 1 (ifeq_axiom) }
% 225.00/32.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(implies(a, b), b)), Y6)), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6)))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(S8, implies(implies(a, implies(implies(a, b), b)), Y6))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, 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% 225.00/32.69 = { by axiom 1 (ifeq_axiom) R->L }
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% 225.00/32.72 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 225.00/32.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), 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% 225.75/32.76 = { by axiom 2 (condensed_detachment) }
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b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 225.75/32.78 = { by axiom 1 (ifeq_axiom) }
% 225.75/32.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8)))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y8, Z8), implies(W8, V8)), implies(implies(V8, Y8), implies(U8, implies(W8, Y8))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 226.04/32.81 = { by axiom 2 (condensed_detachment) }
% 226.04/32.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 226.04/32.83 = { by axiom 1 (ifeq_axiom) }
% 226.04/32.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 226.04/32.85 = { by axiom 1 (ifeq_axiom) R->L }
% 226.04/32.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 226.04/32.88 = { by axiom 2 (condensed_detachment) R->L }
% 226.04/32.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), implies(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), 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% 226.74/32.91 = { by axiom 3 (ic_JLukasiewicz_5) }
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% 226.74/32.94 = { by axiom 1 (ifeq_axiom) }
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% 226.74/32.97 = { by axiom 1 (ifeq_axiom) R->L }
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% 227.44/33.00 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 227.44/33.05 = { by axiom 1 (ifeq_axiom) R->L }
% 227.44/33.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, S9))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), 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% 227.44/33.09 = { by axiom 2 (condensed_detachment) R->L }
% 228.15/33.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, 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% 228.15/33.15 = { by axiom 1 (ifeq_axiom) R->L }
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% 228.85/33.22 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 228.85/33.26 = { by axiom 1 (ifeq_axiom) R->L }
% 228.85/33.29 ifeq(ifeq(ifeq(ifeq(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(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(V10, U10), implies(U10, 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% 229.55/33.31 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, S9)))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, S9)))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, 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is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 229.55/33.36 = { by axiom 2 (condensed_detachment) }
% 229.55/33.38 ifeq(ifeq(ifeq(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(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, is_a_theorem(implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), 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true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 230.25/33.41 = { by axiom 1 (ifeq_axiom) }
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% 230.25/33.48 = { by axiom 1 (ifeq_axiom) R->L }
% 230.25/33.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, 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% 230.96/33.52 = { by axiom 2 (condensed_detachment) R->L }
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% 230.96/33.57 = { by axiom 1 (ifeq_axiom) R->L }
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% 230.96/33.62 = { by axiom 2 (condensed_detachment) R->L }
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% 231.89/33.67 = { by axiom 3 (ic_JLukasiewicz_5) }
% 231.89/33.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(W11, V10)), implies(implies(V10, U10), implies(V11, implies(W11, U10))))), true, is_a_theorem(implies(implies(implies(V11, implies(W11, U10)), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(implies(Y11, T10), implies(Z11, implies(X11, T10)))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), 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% 231.89/33.72 = { by axiom 1 (ifeq_axiom) }
% 232.61/33.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(W11, V10)), implies(implies(V10, U10), implies(V11, implies(W11, U10))))), true, is_a_theorem(implies(implies(implies(V11, implies(W11, U10)), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(implies(Y11, T10), implies(Z11, implies(X11, T10)))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), 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% 232.61/33.78 = { by axiom 3 (ic_JLukasiewicz_5) }
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% 233.08/33.84 = { by axiom 1 (ifeq_axiom) }
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% 233.76/33.90 = { by axiom 1 (ifeq_axiom) R->L }
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implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 233.76/33.96 = { by axiom 2 (condensed_detachment) R->L }
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% 234.47/34.03 = { by axiom 3 (ic_JLukasiewicz_5) }
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% 234.47/34.09 = { by axiom 1 (ifeq_axiom) }
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is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 235.16/34.14 = { by axiom 3 (ic_JLukasiewicz_5) }
% 235.16/34.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V11, implies(W11, U10)), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(V10, U10), implies(U10, implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(implies(T10, S10), implies(X11, Y11)), implies(implies(Y11, T10), implies(Z11, implies(X11, T10)))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), 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% 235.16/34.19 = { by axiom 1 (ifeq_axiom) }
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% 235.88/34.25 = { by axiom 2 (condensed_detachment) }
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% 235.88/34.29 = { by axiom 1 (ifeq_axiom) }
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implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, 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% 236.57/34.33 = { by axiom 3 (ic_JLukasiewicz_5) }
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% 236.57/34.37 = { by axiom 1 (ifeq_axiom) }
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% 237.27/34.41 = { by axiom 1 (ifeq_axiom) R->L }
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% 237.27/34.44 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 237.27/34.47 = { by axiom 2 (condensed_detachment) }
% 237.27/34.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, S9)))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), implies(Y10, Z10)), 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implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 237.99/34.50 = { by axiom 1 (ifeq_axiom) }
% 237.99/34.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), implies(W10, implies(Y10, S9)))), implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(S9, X10), implies(Y10, Z10)), implies(implies(Z10, S9), 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% 237.99/34.53 = { by axiom 2 (condensed_detachment) }
% 237.99/34.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, 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implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 237.99/34.55 = { by axiom 1 (ifeq_axiom) }
% 237.99/34.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, 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% 237.99/34.57 = { by axiom 1 (ifeq_axiom) R->L }
% 237.99/34.58 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), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), 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% 237.99/34.59 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 237.99/34.61 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(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, 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implies(implies(a, b), b)))))))), implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))))), true), true), true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 237.99/34.62 = { by axiom 2 (condensed_detachment) }
% 237.99/34.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 237.99/34.63 = { by axiom 1 (ifeq_axiom) }
% 237.99/34.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 237.99/34.65 = { by axiom 1 (ifeq_axiom) R->L }
% 239.08/34.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.08/34.67 = { by axiom 2 (condensed_detachment) R->L }
% 239.08/34.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.08/34.69 = { by axiom 1 (ifeq_axiom) R->L }
% 239.08/34.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.08/34.71 = { by axiom 2 (condensed_detachment) R->L }
% 239.08/34.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, T7), implies(Z12, S7)), implies(implies(S7, X8), implies(W12, implies(Z12, X8)))), implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true, ifeq(is_a_theorem(implies(implies(implies(X8, T7), implies(Z12, S7)), implies(implies(S7, X8), implies(W12, implies(Z12, X8))))), true, is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.08/34.73 = { by axiom 3 (ic_JLukasiewicz_5) }
% 239.08/34.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X8, T7), implies(Z12, S7)), implies(implies(S7, X8), implies(W12, implies(Z12, X8))))), true, is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.08/34.75 = { by axiom 1 (ifeq_axiom) }
% 239.80/34.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X8, T7), implies(Z12, S7)), implies(implies(S7, X8), implies(W12, implies(Z12, X8))))), true, is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.80/34.77 = { by axiom 3 (ic_JLukasiewicz_5) }
% 239.80/34.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 239.80/34.79 = { by axiom 1 (ifeq_axiom) }
% 239.80/34.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.10/34.81 = { by axiom 1 (ifeq_axiom) R->L }
% 240.10/34.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.10/34.83 = { by axiom 2 (condensed_detachment) R->L }
% 240.10/34.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, implies(implies(S7, X8), implies(X8, T7))), implies(X8, U7)), implies(implies(U7, T7), implies(implies(W12, implies(Z12, X8)), implies(X8, T7)))), implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))))), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(S7, X8), implies(X8, T7))), implies(X8, U7)), implies(implies(U7, T7), implies(implies(W12, implies(Z12, X8)), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.10/34.85 = { by axiom 3 (ic_JLukasiewicz_5) }
% 240.10/34.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(S7, X8), implies(X8, T7))), implies(X8, U7)), implies(implies(U7, T7), implies(implies(W12, implies(Z12, X8)), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.10/34.87 = { by axiom 1 (ifeq_axiom) }
% 240.10/34.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(S7, X8), implies(X8, T7))), implies(X8, U7)), implies(implies(U7, T7), implies(implies(W12, implies(Z12, X8)), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.10/34.89 = { by axiom 3 (ic_JLukasiewicz_5) }
% 240.10/34.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.91 = { by axiom 1 (ifeq_axiom) }
% 240.79/34.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))))), true, ifeq(is_a_theorem(implies(implies(implies(W12, implies(Z12, X8)), implies(X8, T7)), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11)))), implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.92 = { by axiom 2 (condensed_detachment) }
% 240.79/34.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.94 = { by axiom 1 (ifeq_axiom) }
% 240.79/34.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(implies(X12, U11), implies(Y12, implies(S11, U11))))), true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.95 = { by axiom 3 (ic_JLukasiewicz_5) }
% 240.79/34.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.96 = { by axiom 1 (ifeq_axiom) }
% 240.79/34.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7)))), implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(U7, T7), implies(T7, implies(implies(S7, X8), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(Z6, W6), implies(W6, implies(implies(V6, U6), implies(U6, W6)))), implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.97 = { by axiom 2 (condensed_detachment) }
% 240.79/34.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.98 = { by axiom 1 (ifeq_axiom) }
% 240.79/34.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 240.79/34.99 = { by axiom 1 (ifeq_axiom) R->L }
% 240.79/35.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.00 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 241.50/35.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))), implies(a, b)), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.01 = { by axiom 2 (condensed_detachment) }
% 241.50/35.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.02 = { by axiom 1 (ifeq_axiom) }
% 241.50/35.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.02 = { by axiom 1 (ifeq_axiom) R->L }
% 241.50/35.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.03 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 241.50/35.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), Y6), implies(a, b)), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(Z4, W4), implies(W4, implies(implies(V4, U4), implies(U4, W4)))), implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.03 = { by axiom 2 (condensed_detachment) }
% 241.50/35.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.04 = { by axiom 1 (ifeq_axiom) }
% 241.50/35.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.04 = { by axiom 1 (ifeq_axiom) R->L }
% 241.50/35.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.05 = { by axiom 2 (condensed_detachment) R->L }
% 241.50/35.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.05 = { by axiom 1 (ifeq_axiom) R->L }
% 241.50/35.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.06 = { by axiom 2 (condensed_detachment) R->L }
% 241.50/35.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y5, S4), implies(Y13, X5)), implies(implies(X5, Y5), implies(Z13, implies(Y13, Y5)))), implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y5, S4), implies(Y13, X5)), implies(implies(X5, Y5), implies(Z13, implies(Y13, Y5))))), true, is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.07 = { by axiom 3 (ic_JLukasiewicz_5) }
% 241.50/35.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y5, S4), implies(Y13, X5)), implies(implies(X5, Y5), implies(Z13, implies(Y13, Y5))))), true, is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.07 = { by axiom 1 (ifeq_axiom) }
% 241.50/35.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y5, S4), implies(Y13, X5)), implies(implies(X5, Y5), implies(Z13, implies(Y13, Y5))))), true, is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.08 = { by axiom 3 (ic_JLukasiewicz_5) }
% 241.50/35.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.09 = { by axiom 1 (ifeq_axiom) }
% 241.50/35.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 241.50/35.10 = { by axiom 1 (ifeq_axiom) R->L }
% 241.50/35.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.10 = { by axiom 2 (condensed_detachment) R->L }
% 242.22/35.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S4, implies(implies(X5, Y5), implies(Y5, S4))), implies(Y5, T4)), implies(implies(T4, S4), implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)))), implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))))), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(implies(X5, Y5), implies(Y5, S4))), implies(Y5, T4)), implies(implies(T4, S4), implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.11 = { by axiom 3 (ic_JLukasiewicz_5) }
% 242.22/35.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(implies(X5, Y5), implies(Y5, S4))), implies(Y5, T4)), implies(implies(T4, S4), implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.12 = { by axiom 1 (ifeq_axiom) }
% 242.22/35.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S4, implies(implies(X5, Y5), implies(Y5, S4))), implies(Y5, T4)), implies(implies(T4, S4), implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.13 = { by axiom 3 (ic_JLukasiewicz_5) }
% 242.22/35.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.13 = { by axiom 1 (ifeq_axiom) }
% 242.22/35.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z13, implies(Y13, Y5)), implies(Y5, S4)), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12)))), implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.14 = { by axiom 2 (condensed_detachment) }
% 242.22/35.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.14 = { by axiom 1 (ifeq_axiom) }
% 242.22/35.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V12, U12), implies(T12, S12)), implies(implies(S12, V12), implies(X13, implies(T12, V12))))), true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.15 = { by axiom 3 (ic_JLukasiewicz_5) }
% 242.22/35.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.15 = { by axiom 1 (ifeq_axiom) }
% 242.22/35.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4)))), implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(T4, S4), implies(S4, implies(implies(X5, Y5), implies(Y5, S4))))), true, is_a_theorem(implies(implies(b, implies(a, implies(implies(a, b), b))), implies(implies(a, b), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.15 = { by axiom 2 (condensed_detachment) }
% 242.22/35.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.15 = { by axiom 1 (ifeq_axiom) }
% 242.22/35.16 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.16 = { by axiom 1 (ifeq_axiom) R->L }
% 242.22/35.16 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.16 = { by axiom 2 (condensed_detachment) R->L }
% 242.22/35.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.17 = { by axiom 1 (ifeq_axiom) R->L }
% 242.22/35.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.18 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 242.22/35.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.18 = { by axiom 1 (ifeq_axiom) R->L }
% 242.22/35.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.22/35.19 = { by axiom 2 (condensed_detachment) R->L }
% 242.22/35.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))))), true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.20 = { by axiom 1 (ifeq_axiom) R->L }
% 242.92/35.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.21 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 242.92/35.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V13, implies(implies(U13, T13), implies(T13, V13))), implies(T13, W13)), implies(implies(W13, V13), implies(implies(V14, implies(U14, T13)), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.22 = { by axiom 1 (ifeq_axiom) R->L }
% 242.92/35.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V13, implies(implies(U13, T13), implies(T13, V13))), implies(T13, W13)), implies(implies(W13, V13), implies(implies(V14, implies(U14, T13)), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.23 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 242.92/35.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V13, implies(implies(U13, T13), implies(T13, V13))), implies(T13, W13)), implies(implies(W13, V13), implies(implies(V14, implies(U14, T13)), implies(T13, V13)))), implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))))), true, ifeq(is_a_theorem(implies(implies(implies(V13, implies(implies(U13, T13), implies(T13, V13))), implies(T13, W13)), implies(implies(W13, V13), implies(implies(V14, implies(U14, T13)), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.23 = { by axiom 2 (condensed_detachment) }
% 242.92/35.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.24 = { by axiom 1 (ifeq_axiom) }
% 242.92/35.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.25 = { by axiom 1 (ifeq_axiom) R->L }
% 242.92/35.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.26 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 242.92/35.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T13, V13), implies(U14, U13)), implies(implies(U13, T13), implies(V14, implies(U14, T13))))), true, is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.26 = { by axiom 1 (ifeq_axiom) R->L }
% 242.92/35.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T13, V13), implies(U14, U13)), implies(implies(U13, T13), implies(V14, implies(U14, T13))))), true, is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.27 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 242.92/35.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T13, V13), implies(U14, U13)), implies(implies(U13, T13), implies(V14, implies(U14, T13)))), implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true, ifeq(is_a_theorem(implies(implies(implies(T13, V13), implies(U14, U13)), implies(implies(U13, T13), implies(V14, implies(U14, T13))))), true, is_a_theorem(implies(implies(implies(V14, implies(U14, T13)), implies(T13, V13)), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.28 = { by axiom 2 (condensed_detachment) }
% 242.92/35.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.28 = { by axiom 1 (ifeq_axiom) }
% 242.92/35.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13)))), implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))))), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(implies(Z14, S13), implies(W14, implies(Y14, S13))))), true, is_a_theorem(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.29 = { by axiom 2 (condensed_detachment) }
% 242.92/35.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 242.92/35.30 = { by axiom 1 (ifeq_axiom) }
% 242.92/35.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.30 = { by axiom 1 (ifeq_axiom) R->L }
% 243.62/35.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.31 = { by axiom 2 (condensed_detachment) R->L }
% 243.62/35.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.33 = { by axiom 1 (ifeq_axiom) R->L }
% 243.62/35.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.34 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 243.62/35.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.36 = { by axiom 1 (ifeq_axiom) R->L }
% 243.62/35.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 243.62/35.38 = { by axiom 2 (condensed_detachment) R->L }
% 243.62/35.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, 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implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 244.33/35.41 = { by axiom 1 (ifeq_axiom) R->L }
% 244.33/35.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), 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% 244.33/35.44 = { by axiom 2 (condensed_detachment) R->L }
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% 244.33/35.47 = { by axiom 1 (ifeq_axiom) R->L }
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% 245.04/35.50 = { by axiom 2 (condensed_detachment) R->L }
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implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 245.04/35.54 = { by axiom 3 (ic_JLukasiewicz_5) }
% 245.04/35.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(V16, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(U16, implies(V16, a))))), true, is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 245.04/35.59 = { by axiom 1 (ifeq_axiom) }
% 245.04/35.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(V16, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(U16, implies(V16, a))))), true, is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 245.04/35.63 = { by axiom 3 (ic_JLukasiewicz_5) }
% 245.04/35.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 246.12/35.67 = { by axiom 1 (ifeq_axiom) }
% 246.12/35.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, 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b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 246.12/35.72 = { by axiom 1 (ifeq_axiom) R->L }
% 246.12/35.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, 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ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, 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b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 246.86/35.76 = { by axiom 2 (condensed_detachment) R->L }
% 246.86/35.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, 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% 247.15/35.81 = { by axiom 3 (ic_JLukasiewicz_5) }
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implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 247.15/35.85 = { by axiom 1 (ifeq_axiom) }
% 247.15/35.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), implies(a, implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, 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ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 247.15/35.88 = { by axiom 3 (ic_JLukasiewicz_5) }
% 247.85/35.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))))), true), true, 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implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 247.85/35.92 = { by axiom 1 (ifeq_axiom) }
% 247.85/35.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U16, implies(V16, a)), implies(a, 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ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, a)), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, 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implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 247.85/35.95 = { by axiom 2 (condensed_detachment) }
% 247.85/35.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, 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is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 247.85/35.98 = { by axiom 1 (ifeq_axiom) }
% 247.85/35.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 248.55/36.00 = { by axiom 3 (ic_JLukasiewicz_5) }
% 248.55/36.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 248.55/36.03 = { by axiom 1 (ifeq_axiom) }
% 248.55/36.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 248.55/36.05 = { by axiom 1 (ifeq_axiom) R->L }
% 248.55/36.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 248.55/36.07 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 248.55/36.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 248.55/36.09 = { by axiom 2 (condensed_detachment) }
% 248.55/36.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.10 = { by axiom 1 (ifeq_axiom) }
% 249.26/36.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), a), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.11 = { by axiom 3 (ic_JLukasiewicz_5) }
% 249.26/36.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.12 = { by axiom 1 (ifeq_axiom) }
% 249.26/36.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z15, W15), implies(V15, U15)), implies(implies(U15, Z15), implies(T15, implies(V15, Z15))))), true, is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.12 = { by axiom 2 (condensed_detachment) }
% 249.26/36.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.13 = { by axiom 1 (ifeq_axiom) }
% 249.26/36.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.14 = { by axiom 1 (ifeq_axiom) R->L }
% 249.26/36.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.14 = { by axiom 2 (condensed_detachment) R->L }
% 249.26/36.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b))))), true, ifeq(is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.15 = { by axiom 3 (ic_JLukasiewicz_5) }
% 249.26/36.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.16 = { by axiom 1 (ifeq_axiom) }
% 249.26/36.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.17 = { by axiom 1 (ifeq_axiom) R->L }
% 249.26/36.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.18 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 249.26/36.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.26/36.19 = { by axiom 1 (ifeq_axiom) R->L }
% 249.26/36.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.96/36.20 = { by axiom 2 (condensed_detachment) R->L }
% 249.96/36.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.96/36.22 = { by axiom 1 (ifeq_axiom) R->L }
% 249.96/36.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), 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% 249.96/36.23 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 249.96/36.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), b)), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(W17, V17), implies(V17, 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% 249.96/36.25 = { by axiom 1 (ifeq_axiom) R->L }
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% 249.96/36.26 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, 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implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.96/36.28 = { by axiom 2 (condensed_detachment) }
% 249.96/36.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), 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is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 249.96/36.29 = { by axiom 1 (ifeq_axiom) }
% 250.66/36.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), 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implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, 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% 250.66/36.31 = { by axiom 1 (ifeq_axiom) R->L }
% 250.66/36.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, 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implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 250.66/36.33 = { by axiom 2 (condensed_detachment) R->L }
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% 250.66/36.34 = { by axiom 1 (ifeq_axiom) R->L }
% 250.66/36.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, 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% 250.66/36.36 = { by axiom 2 (condensed_detachment) R->L }
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b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 250.66/36.38 = { by axiom 3 (ic_JLukasiewicz_5) }
% 250.66/36.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(Z18, W17)), implies(implies(W17, V17), implies(W18, implies(Z18, V17))))), true, is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), 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is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, 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is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 250.66/36.39 = { by axiom 1 (ifeq_axiom) }
% 251.37/36.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(Z18, W17)), implies(implies(W17, V17), implies(W18, implies(Z18, V17))))), true, is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), 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implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 251.37/36.41 = { by axiom 3 (ic_JLukasiewicz_5) }
% 251.37/36.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, 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is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 251.37/36.44 = { by axiom 1 (ifeq_axiom) }
% 251.37/36.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, 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implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 251.37/36.46 = { by axiom 1 (ifeq_axiom) R->L }
% 251.37/36.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, 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implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 251.37/36.48 = { by axiom 2 (condensed_detachment) R->L }
% 251.37/36.49 ifeq(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, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))), implies(V17, implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))), implies(V17, implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), 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b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, 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b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 252.08/36.50 = { by axiom 3 (ic_JLukasiewicz_5) }
% 252.08/36.51 ifeq(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, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))), implies(V17, implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), 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implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, 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implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 252.08/36.52 = { by axiom 1 (ifeq_axiom) }
% 252.08/36.53 ifeq(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, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))), implies(V17, implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), 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implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, 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% 252.08/36.54 = { by axiom 3 (ic_JLukasiewicz_5) }
% 252.08/36.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, 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T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, 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implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 252.08/36.56 = { by axiom 1 (ifeq_axiom) }
% 252.08/36.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(W18, implies(Z18, V17)), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17)))), implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), 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b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, 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implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, 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% 252.08/36.57 = { by axiom 2 (condensed_detachment) }
% 252.08/36.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, 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implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 252.08/36.59 = { by axiom 1 (ifeq_axiom) }
% 252.08/36.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(implies(X18, U17), implies(Y18, implies(S17, U17))))), true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, 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% 252.08/36.60 = { by axiom 3 (ic_JLukasiewicz_5) }
% 252.08/36.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, 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% 252.08/36.61 = { by axiom 1 (ifeq_axiom) }
% 252.08/36.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 252.08/36.62 = { by axiom 1 (ifeq_axiom) R->L }
% 252.08/36.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, 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implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.63 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 253.01/36.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.65 = { by axiom 2 (condensed_detachment) }
% 253.01/36.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.66 = { by axiom 1 (ifeq_axiom) }
% 253.01/36.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16))))), true, is_a_theorem(implies(implies(b, implies(a, implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.66 = { by axiom 2 (condensed_detachment) }
% 253.01/36.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.67 = { by axiom 1 (ifeq_axiom) }
% 253.01/36.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.67 = { by axiom 1 (ifeq_axiom) R->L }
% 253.01/36.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.68 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 253.01/36.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), b), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(a, implies(a, implies(implies(a, b), b))), b)))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.69 = { by axiom 2 (condensed_detachment) }
% 253.01/36.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.69 = { by axiom 1 (ifeq_axiom) }
% 253.01/36.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.70 = { by axiom 1 (ifeq_axiom) R->L }
% 253.01/36.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.70 = { by axiom 2 (condensed_detachment) R->L }
% 253.01/36.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.71 = { by axiom 1 (ifeq_axiom) R->L }
% 253.01/36.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.71 = { by axiom 2 (condensed_detachment) R->L }
% 253.01/36.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y15, S14), implies(Y19, X15)), implies(implies(X15, Y15), implies(Z19, implies(Y19, Y15)))), implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y15, S14), implies(Y19, X15)), implies(implies(X15, Y15), implies(Z19, implies(Y19, Y15))))), true, is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.72 = { by axiom 3 (ic_JLukasiewicz_5) }
% 253.01/36.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y15, S14), implies(Y19, X15)), implies(implies(X15, Y15), implies(Z19, implies(Y19, Y15))))), true, is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.72 = { by axiom 1 (ifeq_axiom) }
% 253.01/36.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, S14), implies(Y19, X15)), implies(implies(X15, Y15), implies(Z19, implies(Y19, Y15))))), true, is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.01/36.73 = { by axiom 3 (ic_JLukasiewicz_5) }
% 253.01/36.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.73 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.74 = { by axiom 1 (ifeq_axiom) R->L }
% 253.73/36.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.75 = { by axiom 2 (condensed_detachment) R->L }
% 253.73/36.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S14, implies(implies(X15, Y15), implies(Y15, S14))), implies(Y15, T14)), implies(implies(T14, S14), implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)))), implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))))), true, ifeq(is_a_theorem(implies(implies(implies(S14, implies(implies(X15, Y15), implies(Y15, S14))), implies(Y15, T14)), implies(implies(T14, S14), implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.75 = { by axiom 3 (ic_JLukasiewicz_5) }
% 253.73/36.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S14, implies(implies(X15, Y15), implies(Y15, S14))), implies(Y15, T14)), implies(implies(T14, S14), implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.76 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S14, implies(implies(X15, Y15), implies(Y15, S14))), implies(Y15, T14)), implies(implies(T14, S14), implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.76 = { by axiom 3 (ic_JLukasiewicz_5) }
% 253.73/36.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.77 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z19, implies(Y19, Y15)), implies(Y15, S14)), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18)))), implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.77 = { by axiom 2 (condensed_detachment) }
% 253.73/36.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.78 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V18, U18), implies(T18, S18)), implies(implies(S18, V18), implies(X19, implies(T18, V18))))), true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.78 = { by axiom 3 (ic_JLukasiewicz_5) }
% 253.73/36.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.78 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14)))), implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(T14, S14), implies(S14, implies(implies(X15, Y15), implies(Y15, S14))))), true, is_a_theorem(implies(implies(implies(W13, V13), implies(V13, implies(implies(U13, T13), implies(T13, V13)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.78 = { by axiom 2 (condensed_detachment) }
% 253.73/36.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.79 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.79 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), b), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(a, implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.79 = { by axiom 2 (condensed_detachment) }
% 253.73/36.79 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.79 = { by axiom 1 (ifeq_axiom) }
% 253.73/36.79 ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.79 = { by axiom 1 (ifeq_axiom) R->L }
% 253.73/36.79 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.79 = { by axiom 2 (condensed_detachment) R->L }
% 253.73/36.79 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 253.73/36.80 = { by axiom 1 (ifeq_axiom) R->L }
% 253.73/36.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.80 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.80 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.81 = { by axiom 2 (condensed_detachment) R->L }
% 254.21/36.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))))), true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.81 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.81 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V19, implies(implies(U19, T19), implies(T19, V19))), implies(T19, W19)), implies(implies(W19, V19), implies(implies(V20, implies(U20, T19)), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.82 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V19, implies(implies(U19, T19), implies(T19, V19))), implies(T19, W19)), implies(implies(W19, V19), implies(implies(V20, implies(U20, T19)), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.82 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V19, implies(implies(U19, T19), implies(T19, V19))), implies(T19, W19)), implies(implies(W19, V19), implies(implies(V20, implies(U20, T19)), implies(T19, V19)))), implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))))), true, ifeq(is_a_theorem(implies(implies(implies(V19, implies(implies(U19, T19), implies(T19, V19))), implies(T19, W19)), implies(implies(W19, V19), implies(implies(V20, implies(U20, T19)), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.83 = { by axiom 2 (condensed_detachment) }
% 254.21/36.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.83 = { by axiom 1 (ifeq_axiom) }
% 254.21/36.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.83 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.84 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T19, V19), implies(U20, U19)), implies(implies(U19, T19), implies(V20, implies(U20, T19))))), true, is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.85 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T19, V19), implies(U20, U19)), implies(implies(U19, T19), implies(V20, implies(U20, T19))))), true, is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.86 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T19, V19), implies(U20, U19)), implies(implies(U19, T19), implies(V20, implies(U20, T19)))), implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true, ifeq(is_a_theorem(implies(implies(implies(T19, V19), implies(U20, U19)), implies(implies(U19, T19), implies(V20, implies(U20, T19))))), true, is_a_theorem(implies(implies(implies(V20, implies(U20, T19)), implies(T19, V19)), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.86 = { by axiom 2 (condensed_detachment) }
% 254.21/36.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.86 = { by axiom 1 (ifeq_axiom) }
% 254.21/36.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19)))), implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))))), true, ifeq(is_a_theorem(implies(implies(implies(S19, X20), implies(Y20, Z20)), implies(implies(Z20, S19), implies(W20, implies(Y20, S19))))), true, is_a_theorem(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.86 = { by axiom 2 (condensed_detachment) }
% 254.21/36.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.87 = { by axiom 1 (ifeq_axiom) }
% 254.21/36.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.87 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.87 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.88 = { by axiom 2 (condensed_detachment) R->L }
% 254.21/36.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.88 = { by axiom 1 (ifeq_axiom) R->L }
% 254.21/36.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.21/36.89 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 254.21/36.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.91/36.90 = { by axiom 1 (ifeq_axiom) R->L }
% 254.91/36.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.91/36.91 = { by axiom 2 (condensed_detachment) R->L }
% 254.91/36.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 254.91/36.93 = { by axiom 1 (ifeq_axiom) R->L }
% 254.91/36.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, 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implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), 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% 254.91/36.95 = { by axiom 2 (condensed_detachment) R->L }
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% 254.91/36.96 = { by axiom 1 (ifeq_axiom) R->L }
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% 254.91/36.98 = { by axiom 2 (condensed_detachment) R->L }
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Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 255.62/37.01 = { by axiom 3 (ic_JLukasiewicz_5) }
% 255.62/37.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 255.62/37.03 = { by axiom 1 (ifeq_axiom) }
% 255.62/37.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 255.62/37.05 = { by axiom 1 (ifeq_axiom) R->L }
% 255.62/37.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), 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implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 255.62/37.08 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 255.62/37.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 256.32/37.10 = { by axiom 1 (ifeq_axiom) R->L }
% 256.32/37.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, 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Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, 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b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 256.32/37.13 = { by axiom 2 (condensed_detachment) R->L }
% 256.32/37.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U23, implies(T23, S22)), implies(S22, implies(implies(S21, 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% 256.32/37.16 = { by axiom 1 (ifeq_axiom) R->L }
% 256.32/37.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U23, implies(T23, S22)), implies(S22, 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% 256.32/37.20 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 257.02/37.22 = { by axiom 1 (ifeq_axiom) R->L }
% 257.02/37.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), implies(S22, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(U23, implies(T23, S22)), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true, is_a_theorem(implies(implies(implies(implies(U23, implies(T23, S22)), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), implies(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U23, implies(T23, S22)), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true, is_a_theorem(implies(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, 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implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 257.02/37.25 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 257.02/37.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S21, X22), implies(X22, 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U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), 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% 257.02/37.28 = { by axiom 2 (condensed_detachment) }
% 257.02/37.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U23, implies(T23, S22)), implies(S22, 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implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, 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% 257.73/37.31 = { by axiom 1 (ifeq_axiom) }
% 257.73/37.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U23, implies(T23, S22)), implies(S22, implies(implies(S21, X22), 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% 257.73/37.33 = { by axiom 1 (ifeq_axiom) R->L }
% 257.73/37.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U23, implies(T23, S22)), implies(S22, 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% 257.73/37.36 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 257.73/37.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S22, implies(implies(S21, X22), implies(X22, 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implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 257.73/37.38 = { by axiom 1 (ifeq_axiom) R->L }
% 257.73/37.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S22, implies(implies(S21, X22), implies(X22, 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% 258.43/37.41 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 258.43/37.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S22, implies(implies(S21, X22), implies(X22, 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implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 258.43/37.43 = { by axiom 2 (condensed_detachment) }
% 258.43/37.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 258.43/37.45 = { by axiom 1 (ifeq_axiom) }
% 258.43/37.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(X23, Y23), implies(Z23, W23)), implies(implies(W23, X23), implies(V23, implies(Z23, X23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 258.43/37.47 = { by axiom 2 (condensed_detachment) }
% 258.43/37.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, 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implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 259.13/37.50 = { by axiom 1 (ifeq_axiom) }
% 259.13/37.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, 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% 259.13/37.52 = { by axiom 1 (ifeq_axiom) R->L }
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% 259.13/37.55 = { by axiom 2 (condensed_detachment) R->L }
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implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, 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true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 259.13/37.57 = { by axiom 3 (ic_JLukasiewicz_5) }
% 259.13/37.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), 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Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, 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% 259.13/37.60 = { by axiom 1 (ifeq_axiom) }
% 259.13/37.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), 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ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, 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is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, 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true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 259.13/37.62 = { by axiom 3 (ic_JLukasiewicz_5) }
% 259.13/37.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, 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b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.64 = { by axiom 1 (ifeq_axiom) }
% 260.04/37.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, 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implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T22, S22), implies(S22, implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.66 = { by axiom 2 (condensed_detachment) }
% 260.04/37.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.67 = { by axiom 1 (ifeq_axiom) }
% 260.04/37.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y22, Z22), implies(W22, V22)), implies(implies(V22, Y22), implies(U22, implies(W22, Y22))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.68 = { by axiom 3 (ic_JLukasiewicz_5) }
% 260.04/37.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.71 = { by axiom 1 (ifeq_axiom) }
% 260.04/37.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.04/37.72 = { by axiom 1 (ifeq_axiom) R->L }
% 260.04/37.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.77/37.73 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 260.77/37.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(a, implies(implies(a, b), b))), implies(implies(a, implies(implies(a, b), b)), implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.77/37.75 = { by axiom 2 (condensed_detachment) }
% 260.77/37.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.77/37.76 = { by axiom 1 (ifeq_axiom) }
% 260.77/37.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.77/37.77 = { by axiom 1 (ifeq_axiom) R->L }
% 260.77/37.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 260.77/37.78 = { by axiom 2 (condensed_detachment) R->L }
% 260.77/37.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, 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U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, 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% 260.77/37.79 = { by axiom 1 (ifeq_axiom) R->L }
% 261.24/37.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), 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% 261.24/37.81 = { by axiom 2 (condensed_detachment) R->L }
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b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.24/37.82 = { by axiom 3 (ic_JLukasiewicz_5) }
% 261.24/37.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(V24, S21)), implies(implies(S21, X22), implies(U24, implies(V24, X22))))), true, is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.24/37.84 = { by axiom 1 (ifeq_axiom) }
% 261.24/37.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(V24, S21)), implies(implies(S21, X22), implies(U24, implies(V24, X22))))), true, is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.24/37.85 = { by axiom 3 (ic_JLukasiewicz_5) }
% 261.24/37.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), 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true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.24/37.87 = { by axiom 1 (ifeq_axiom) }
% 261.24/37.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.24/37.88 = { by axiom 1 (ifeq_axiom) R->L }
% 261.24/37.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), 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is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), 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% 261.95/37.90 = { by axiom 2 (condensed_detachment) R->L }
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b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, 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Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.92 = { by axiom 3 (ic_JLukasiewicz_5) }
% 261.95/37.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), 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implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, 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Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.94 = { by axiom 1 (ifeq_axiom) }
% 261.95/37.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), 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implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), 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Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.95 = { by axiom 3 (ic_JLukasiewicz_5) }
% 261.95/37.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.96 = { by axiom 1 (ifeq_axiom) }
% 261.95/37.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, X22)), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.98 = { by axiom 2 (condensed_detachment) }
% 261.95/37.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 261.95/37.99 = { by axiom 1 (ifeq_axiom) }
% 261.95/37.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(implies(Z24, S23), implies(W24, implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.00 = { by axiom 3 (ic_JLukasiewicz_5) }
% 262.65/38.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.01 = { by axiom 1 (ifeq_axiom) }
% 262.65/38.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.02 = { by axiom 1 (ifeq_axiom) R->L }
% 262.65/38.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.03 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 262.65/38.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))))), implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))), implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y))))))))), true, is_a_theorem(implies(implies(implies(implies(S21, X22), implies(X22, implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.04 = { by axiom 2 (condensed_detachment) }
% 262.65/38.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.04 = { by axiom 1 (ifeq_axiom) }
% 262.65/38.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21)))), implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z21, W21), implies(V21, U21)), implies(implies(U21, Z21), implies(T21, implies(V21, Z21))))), true, is_a_theorem(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.05 = { by axiom 2 (condensed_detachment) }
% 262.65/38.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.05 = { by axiom 1 (ifeq_axiom) }
% 262.65/38.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.06 = { by axiom 1 (ifeq_axiom) R->L }
% 262.65/38.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.06 = { by axiom 2 (condensed_detachment) R->L }
% 262.65/38.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.07 = { by axiom 3 (ic_JLukasiewicz_5) }
% 262.65/38.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.08 = { by axiom 1 (ifeq_axiom) }
% 262.65/38.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.08 = { by axiom 1 (ifeq_axiom) R->L }
% 262.65/38.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 262.65/38.09 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 263.36/38.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.10 = { by axiom 1 (ifeq_axiom) R->L }
% 263.36/38.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.11 = { by axiom 2 (condensed_detachment) R->L }
% 263.36/38.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.13 = { by axiom 3 (ic_JLukasiewicz_5) }
% 263.36/38.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.14 = { by axiom 1 (ifeq_axiom) }
% 263.36/38.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.15 = { by axiom 1 (ifeq_axiom) R->L }
% 263.36/38.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.17 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 263.36/38.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 263.36/38.18 = { by axiom 1 (ifeq_axiom) R->L }
% 263.36/38.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.05/38.20 = { by axiom 2 (condensed_detachment) R->L }
% 264.05/38.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, 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implies(S, U)))), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), 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U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, 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is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.05/38.22 = { by axiom 1 (ifeq_axiom) R->L }
% 264.05/38.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, 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b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.05/38.24 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 264.05/38.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(implies(V25, 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implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.05/38.26 = { by axiom 1 (ifeq_axiom) R->L }
% 264.05/38.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, 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U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.05/38.28 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 264.05/38.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))), implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), 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S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, 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implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 264.77/38.30 = { by axiom 2 (condensed_detachment) }
% 264.77/38.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, 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implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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% 264.77/38.32 = { by axiom 1 (ifeq_axiom) }
% 264.77/38.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, 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implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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% 264.77/38.33 = { by axiom 1 (ifeq_axiom) R->L }
% 264.77/38.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, 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is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, 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% 264.77/38.35 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 264.77/38.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a), implies(U25, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), 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% 264.77/38.36 = { by axiom 1 (ifeq_axiom) R->L }
% 264.77/38.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a), implies(U25, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true), true, 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implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, 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% 264.77/38.38 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 264.77/38.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a), implies(U25, implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(V25, implies(U25, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true, 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% 264.77/38.39 = { by axiom 2 (condensed_detachment) }
% 265.48/38.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), 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implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.40 = { by axiom 1 (ifeq_axiom) }
% 265.48/38.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24)))), implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(S24, X25), implies(Y25, Z25)), implies(implies(Z25, S24), implies(W25, implies(Y25, S24))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), a), implies(a, implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.41 = { by axiom 2 (condensed_detachment) }
% 265.48/38.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.42 = { by axiom 1 (ifeq_axiom) }
% 265.48/38.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), a)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), b), T24), implies(a, implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.43 = { by axiom 2 (condensed_detachment) }
% 265.48/38.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.43 = { by axiom 1 (ifeq_axiom) }
% 265.48/38.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.44 = { by axiom 1 (ifeq_axiom) R->L }
% 265.48/38.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.44 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 265.48/38.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b)))), implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), implies(implies(a, b), b)), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(a, implies(implies(a, b), b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(a, b), b)), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))))), true), true), true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.45 = { by axiom 2 (condensed_detachment) }
% 265.48/38.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.45 = { by axiom 1 (ifeq_axiom) }
% 265.48/38.45 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.46 = { by axiom 1 (ifeq_axiom) R->L }
% 265.48/38.46 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.46 = { by axiom 2 (condensed_detachment) R->L }
% 265.48/38.46 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.46 = { by axiom 1 (ifeq_axiom) R->L }
% 265.48/38.47 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.47 = { by axiom 2 (condensed_detachment) R->L }
% 265.48/38.47 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y21, S20), implies(W26, X21)), implies(implies(X21, Y21), implies(V26, implies(W26, Y21)))), implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y21, S20), implies(W26, X21)), implies(implies(X21, Y21), implies(V26, implies(W26, Y21))))), true, is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.47 = { by axiom 3 (ic_JLukasiewicz_5) }
% 265.48/38.47 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y21, S20), implies(W26, X21)), implies(implies(X21, Y21), implies(V26, implies(W26, Y21))))), true, is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.48 = { by axiom 1 (ifeq_axiom) }
% 265.48/38.49 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y21, S20), implies(W26, X21)), implies(implies(X21, Y21), implies(V26, implies(W26, Y21))))), true, is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 265.48/38.49 = { by axiom 3 (ic_JLukasiewicz_5) }
% 265.48/38.49 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.50 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.50 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.50 = { by axiom 1 (ifeq_axiom) R->L }
% 266.17/38.50 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.51 = { by axiom 2 (condensed_detachment) R->L }
% 266.17/38.51 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(X21, Y21), implies(Y21, S20))), implies(Y21, T20)), implies(implies(T20, S20), implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)))), implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))))), true, ifeq(is_a_theorem(implies(implies(implies(S20, implies(implies(X21, Y21), implies(Y21, S20))), implies(Y21, T20)), implies(implies(T20, S20), implies(implies(V26, implies(W26, Y21)), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.51 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.51 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S20, implies(implies(X21, Y21), implies(Y21, S20))), implies(Y21, T20)), implies(implies(T20, S20), implies(implies(V26, implies(W26, Y21)), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.52 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.52 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S20, implies(implies(X21, Y21), implies(Y21, S20))), implies(Y21, T20)), implies(implies(T20, S20), implies(implies(V26, implies(W26, Y21)), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.52 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.52 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.53 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.53 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))))), true, ifeq(is_a_theorem(implies(implies(implies(V26, implies(W26, Y21)), implies(Y21, S20)), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25)))), implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.53 = { by axiom 2 (condensed_detachment) }
% 266.17/38.53 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.53 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.53 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T25, S25), implies(X26, Y26)), implies(implies(Y26, T25), implies(Z26, implies(X26, T25))))), true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.53 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.53 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.54 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20)))), implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))))), true, ifeq(is_a_theorem(implies(implies(T20, S20), implies(S20, implies(implies(X21, Y21), implies(Y21, S20))))), true, is_a_theorem(implies(implies(implies(W19, V19), implies(V19, implies(implies(U19, T19), implies(T19, V19)))), implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))))), true), true), true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 2 (condensed_detachment) }
% 266.17/38.54 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.54 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(a, implies(implies(a, b), b))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))))), true, ifeq(is_a_theorem(implies(a, implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 2 (condensed_detachment) }
% 266.17/38.54 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) R->L }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.54 = { by axiom 2 (condensed_detachment) R->L }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) R->L }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.54 = { by axiom 2 (condensed_detachment) R->L }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, U), implies(Z27, T)), implies(implies(T, S), implies(W27, implies(Z27, S)))), implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))))), true, ifeq(is_a_theorem(implies(implies(implies(S, U), implies(Z27, T)), implies(implies(T, S), implies(W27, implies(Z27, S))))), true, is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.54 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.54 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S, U), implies(Z27, T)), implies(implies(T, S), implies(W27, implies(Z27, S))))), true, is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.54 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, U), implies(Z27, T)), implies(implies(T, S), implies(W27, implies(Z27, S))))), true, is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 1 (ifeq_axiom) R->L }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 2 (condensed_detachment) R->L }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, implies(implies(T, S), implies(S, U))), implies(S, V)), implies(implies(V, U), implies(implies(W27, implies(Z27, S)), implies(S, U)))), implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(implies(T, S), implies(S, U))), implies(S, V)), implies(implies(V, U), implies(implies(W27, implies(Z27, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.55 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U, implies(implies(T, S), implies(S, U))), implies(S, V)), implies(implies(V, U), implies(implies(W27, implies(Z27, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.55 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U, implies(implies(T, S), implies(S, U))), implies(S, V)), implies(implies(V, U), implies(implies(W27, implies(Z27, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true, ifeq(is_a_theorem(implies(implies(implies(W27, implies(Z27, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 2 (condensed_detachment) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U26, T26), implies(S26, X27)), implies(implies(X27, U26), implies(Y27, implies(S26, U26))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 3 (ic_JLukasiewicz_5) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 1 (ifeq_axiom) }
% 266.17/38.56 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(implies(a, b), b)))), true, ifeq(is_a_theorem(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(a, implies(implies(a, b), b))), true), true)
% 266.17/38.56 = { by axiom 2 (condensed_detachment) }
% 266.17/38.56 true
% 266.17/38.56 % SZS output end Proof
% 266.17/38.56
% 266.17/38.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------