%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:00 AM UTC 2026
% Result : Unsatisfiable 1.68s 0.70s
% Output : Proof 45.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n001.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 15:27:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.68/0.70 Command-line arguments: --no-flatten-goal
% 1.68/0.70
% 1.68/0.70 % SZS status Unsatisfiable
% 1.68/0.70
% 42.12/8.24 % SZS output start Proof
% 42.12/8.24 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 42.12/8.24 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 42.32/8.38 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.
% 42.32/8.38
% 42.32/8.38 Goal 1 (prove_ic_2): is_a_theorem(implies(a, implies(b, a))) = true.
% 42.32/8.38 Proof:
% 42.32/8.38 is_a_theorem(implies(a, implies(b, a)))
% 42.32/8.38 = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/8.38 ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.38 = { by axiom 2 (condensed_detachment) R->L }
% 42.32/8.38 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.38 = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/8.38 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.38 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.32/8.38 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.39 = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/8.39 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.39 = { by axiom 2 (condensed_detachment) R->L }
% 42.32/8.39 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.39 = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/8.39 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.39 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.32/8.40 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.40 = { by axiom 1 (ifeq_axiom) R->L }
% 42.32/8.40 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.32/8.40 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.53/8.40 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.40 = { by axiom 2 (condensed_detachment) }
% 42.53/8.41 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.41 = { by axiom 1 (ifeq_axiom) }
% 42.53/8.41 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.41 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.41 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.41 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.53/8.42 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.42 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.42 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.42 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.53/8.42 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.42 = { by axiom 2 (condensed_detachment) }
% 42.53/8.42 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.42 = { by axiom 1 (ifeq_axiom) }
% 42.53/8.42 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(b, a))))), 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(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.42 = { by axiom 2 (condensed_detachment) }
% 42.53/8.43 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(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.43 = { by axiom 1 (ifeq_axiom) }
% 42.53/8.43 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(b, a))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.43 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.43 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.43 = { by axiom 2 (condensed_detachment) R->L }
% 42.53/8.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.44 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.45 = { by axiom 2 (condensed_detachment) R->L }
% 42.53/8.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.45 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.46 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.53/8.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.47 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.48 = { by axiom 2 (condensed_detachment) R->L }
% 42.53/8.48 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))))), true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.49 = { by axiom 1 (ifeq_axiom) R->L }
% 42.53/8.50 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.53/8.50 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.75/8.51 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V3, implies(implies(U3, T3), implies(T3, V3))), implies(T3, W3)), implies(implies(W3, V3), implies(implies(X5, implies(Y5, T3)), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.51 = { by axiom 1 (ifeq_axiom) R->L }
% 42.75/8.51 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(implies(U3, T3), implies(T3, V3))), implies(T3, W3)), implies(implies(W3, V3), implies(implies(X5, implies(Y5, T3)), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.52 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.75/8.53 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V3, implies(implies(U3, T3), implies(T3, V3))), implies(T3, W3)), implies(implies(W3, V3), implies(implies(X5, implies(Y5, T3)), implies(T3, V3)))), implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))))), true, ifeq(is_a_theorem(implies(implies(implies(V3, implies(implies(U3, T3), implies(T3, V3))), implies(T3, W3)), implies(implies(W3, V3), implies(implies(X5, implies(Y5, T3)), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.53 = { by axiom 2 (condensed_detachment) }
% 42.75/8.54 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.54 = { by axiom 1 (ifeq_axiom) }
% 42.75/8.54 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.55 = { by axiom 1 (ifeq_axiom) R->L }
% 42.75/8.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.56 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.75/8.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T3, V3), implies(Y5, U3)), implies(implies(U3, T3), implies(X5, implies(Y5, T3))))), true, is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.57 = { by axiom 1 (ifeq_axiom) R->L }
% 42.75/8.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T3, V3), implies(Y5, U3)), implies(implies(U3, T3), implies(X5, implies(Y5, T3))))), true, is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.58 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.75/8.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, V3), implies(Y5, U3)), implies(implies(U3, T3), implies(X5, implies(Y5, T3)))), implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true, ifeq(is_a_theorem(implies(implies(implies(T3, V3), implies(Y5, U3)), implies(implies(U3, T3), implies(X5, implies(Y5, T3))))), true, is_a_theorem(implies(implies(implies(X5, implies(Y5, T3)), implies(T3, V3)), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.58 = { by axiom 2 (condensed_detachment) }
% 42.75/8.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.59 = { by axiom 1 (ifeq_axiom) }
% 42.75/8.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4)))), implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))))), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(implies(T4, W4), implies(S4, implies(U4, W4))))), true, is_a_theorem(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.75/8.60 = { by axiom 2 (condensed_detachment) }
% 42.75/8.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.61 = { by axiom 1 (ifeq_axiom) }
% 42.95/8.61 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.62 = { by axiom 1 (ifeq_axiom) R->L }
% 42.95/8.62 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.62 = { by axiom 2 (condensed_detachment) R->L }
% 42.95/8.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.63 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.95/8.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.65 = { by axiom 1 (ifeq_axiom) }
% 42.95/8.65 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.66 = { by axiom 1 (ifeq_axiom) R->L }
% 42.95/8.66 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.67 = { by axiom 2 (condensed_detachment) R->L }
% 42.95/8.67 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.68 = { by axiom 1 (ifeq_axiom) R->L }
% 42.95/8.69 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 42.95/8.70 = { by axiom 2 (condensed_detachment) R->L }
% 43.15/8.71 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, 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)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.71 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.15/8.72 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, 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)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.73 = { by axiom 1 (ifeq_axiom) }
% 43.15/8.73 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, 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)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.74 = { by axiom 1 (ifeq_axiom) R->L }
% 43.15/8.75 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(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), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.76 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.15/8.76 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.77 = { by axiom 1 (ifeq_axiom) R->L }
% 43.15/8.77 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.78 = { by axiom 2 (condensed_detachment) R->L }
% 43.15/8.79 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.15/8.79 = { by axiom 1 (ifeq_axiom) R->L }
% 43.15/8.80 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), 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implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.81 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.25/8.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))), implies(X6, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.82 = { by axiom 1 (ifeq_axiom) R->L }
% 43.25/8.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))), implies(X6, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.83 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.25/8.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))), implies(X6, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))))), implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))), implies(X6, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.85 = { by axiom 2 (condensed_detachment) }
% 43.25/8.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.86 = { by axiom 1 (ifeq_axiom) }
% 43.25/8.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.87 = { by axiom 1 (ifeq_axiom) R->L }
% 43.25/8.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.88 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.25/8.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X6, implies(b, a)), implies(S6, S5)), implies(implies(S5, X6), implies(T6, implies(S6, X6))))), true, is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.25/8.89 = { by axiom 1 (ifeq_axiom) R->L }
% 43.25/8.90 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X6, implies(b, a)), implies(S6, S5)), implies(implies(S5, X6), implies(T6, implies(S6, X6))))), true, is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.90 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.36/8.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X6, implies(b, a)), implies(S6, S5)), implies(implies(S5, X6), implies(T6, implies(S6, X6)))), implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(X6, implies(b, a)), implies(S6, S5)), implies(implies(S5, X6), implies(T6, implies(S6, X6))))), true, is_a_theorem(implies(implies(implies(T6, implies(S6, X6)), implies(X6, implies(b, a))), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.91 = { by axiom 2 (condensed_detachment) }
% 43.36/8.92 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.92 = { by axiom 1 (ifeq_axiom) }
% 43.36/8.93 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(implies(V6, Y6), implies(U6, implies(W6, Y6))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(b, a)), implies(implies(b, a), implies(implies(S5, X6), implies(X6, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.93 = { by axiom 2 (condensed_detachment) }
% 43.36/8.94 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.95 = { by axiom 1 (ifeq_axiom) }
% 43.36/8.95 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.96 = { by axiom 1 (ifeq_axiom) R->L }
% 43.36/8.96 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.97 = { by axiom 2 (condensed_detachment) R->L }
% 43.36/8.98 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(b, a))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(b, a))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.98 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.36/8.99 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(b, a))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, 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implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/8.99 = { by axiom 1 (ifeq_axiom) }
% 43.36/9.00 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(b, a))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.00 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.36/9.01 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.01 = { by axiom 1 (ifeq_axiom) }
% 43.36/9.02 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S5, X6), implies(X6, implies(b, a))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z5, W5), implies(V5, U5)), implies(implies(U5, Z5), implies(T5, implies(V5, Z5)))), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.02 = { by axiom 2 (condensed_detachment) }
% 43.36/9.02 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.03 = { by axiom 1 (ifeq_axiom) }
% 43.36/9.03 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(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(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.03 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.36/9.04 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.04 = { by axiom 1 (ifeq_axiom) }
% 43.36/9.04 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.05 = { by axiom 1 (ifeq_axiom) R->L }
% 43.36/9.05 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.36/9.05 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.36/9.06 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(b, a)), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(a, implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.06 = { by axiom 2 (condensed_detachment) }
% 43.54/9.06 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.06 = { by axiom 1 (ifeq_axiom) }
% 43.54/9.07 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.07 = { by axiom 1 (ifeq_axiom) R->L }
% 43.54/9.07 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.08 = { by axiom 2 (condensed_detachment) R->L }
% 43.54/9.08 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.09 = { by axiom 1 (ifeq_axiom) R->L }
% 43.54/9.09 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.10 = { by axiom 2 (condensed_detachment) R->L }
% 43.54/9.10 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.11 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.54/9.11 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.12 = { by axiom 1 (ifeq_axiom) }
% 43.54/9.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.13 = { by axiom 1 (ifeq_axiom) R->L }
% 43.54/9.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.14 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.54/9.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.54/9.15 = { by axiom 1 (ifeq_axiom) R->L }
% 43.54/9.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.64/9.16 = { by axiom 2 (condensed_detachment) R->L }
% 43.64/9.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.64/9.19 = { by axiom 1 (ifeq_axiom) R->L }
% 43.64/9.20 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.21 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.68/9.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), implies(T7, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(V8, implies(U8, T7)), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.22 = { by axiom 1 (ifeq_axiom) R->L }
% 43.68/9.23 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), 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(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), implies(T7, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(V8, implies(U8, T7)), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.24 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.68/9.25 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), implies(T7, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(V8, implies(U8, T7)), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), implies(T7, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(implies(V8, implies(U8, T7)), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))), implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.25 = { by axiom 2 (condensed_detachment) }
% 43.68/9.26 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.26 = { by axiom 1 (ifeq_axiom) }
% 43.68/9.27 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.28 = { by axiom 1 (ifeq_axiom) R->L }
% 43.68/9.28 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.29 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.68/9.29 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(U8, U7)), implies(implies(U7, T7), implies(V8, implies(U8, T7))))), true, is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.68/9.30 = { by axiom 1 (ifeq_axiom) R->L }
% 43.78/9.30 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(U8, U7)), implies(implies(U7, T7), implies(V8, implies(U8, T7))))), true, is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.31 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.78/9.32 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(U8, U7)), implies(implies(U7, T7), implies(V8, implies(U8, T7)))), implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))), implies(U8, U7)), implies(implies(U7, T7), implies(V8, implies(U8, T7))))), true, is_a_theorem(implies(implies(implies(V8, implies(U8, T7)), implies(T7, 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.32 = { by axiom 2 (condensed_detachment) }
% 43.78/9.33 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.33 = { by axiom 1 (ifeq_axiom) }
% 43.78/9.34 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7)))), implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(S7, X8), implies(Y8, Z8)), implies(implies(Z8, S7), implies(W8, implies(Y8, S7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), 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)))), implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.34 = { by axiom 2 (condensed_detachment) }
% 43.78/9.35 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.35 = { by axiom 1 (ifeq_axiom) }
% 43.78/9.36 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.36 = { by axiom 1 (ifeq_axiom) R->L }
% 43.78/9.37 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.37 = { by axiom 2 (condensed_detachment) R->L }
% 43.78/9.38 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.38 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.78/9.39 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.78/9.39 = { by axiom 1 (ifeq_axiom) }
% 43.78/9.40 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.40 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.89/9.41 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.42 = { by axiom 1 (ifeq_axiom) }
% 43.89/9.43 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, T7), implies(T7, implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), implies(a, implies(b, a))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7)))), implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.43 = { by axiom 2 (condensed_detachment) }
% 43.89/9.43 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.44 = { by axiom 1 (ifeq_axiom) }
% 43.89/9.44 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(implies(W7, X7), implies(V7, implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.45 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.89/9.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.45 = { by axiom 1 (ifeq_axiom) }
% 43.89/9.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, a)), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(W3, V3), implies(V3, implies(implies(U3, T3), implies(T3, V3)))), implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.46 = { by axiom 2 (condensed_detachment) }
% 43.89/9.46 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.47 = { by axiom 1 (ifeq_axiom) }
% 43.89/9.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.47 = { by axiom 1 (ifeq_axiom) R->L }
% 43.89/9.47 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.48 = { by axiom 2 (condensed_detachment) R->L }
% 43.89/9.48 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.48 = { by axiom 1 (ifeq_axiom) R->L }
% 43.89/9.49 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.49 = { by axiom 2 (condensed_detachment) R->L }
% 43.89/9.49 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z4, X4), implies(W9, Y4)), implies(implies(Y4, Z4), implies(V9, implies(W9, Z4)))), implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z4, X4), implies(W9, Y4)), implies(implies(Y4, Z4), implies(V9, implies(W9, Z4))))), true, is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.89/9.50 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.89/9.50 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z4, X4), implies(W9, Y4)), implies(implies(Y4, Z4), implies(V9, implies(W9, Z4))))), true, is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.51 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.51 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z4, X4), implies(W9, Y4)), implies(implies(Y4, Z4), implies(V9, implies(W9, Z4))))), true, is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.51 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.99/9.52 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.52 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.53 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.53 = { by axiom 1 (ifeq_axiom) R->L }
% 43.99/9.53 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.54 = { by axiom 2 (condensed_detachment) R->L }
% 43.99/9.54 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))), implies(Z4, S3)), implies(implies(S3, X4), implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)))), implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))))), true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))), implies(Z4, S3)), implies(implies(S3, X4), implies(implies(V9, implies(W9, Z4)), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.55 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.99/9.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))), implies(Z4, S3)), implies(implies(S3, X4), implies(implies(V9, implies(W9, Z4)), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.56 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.56 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))), implies(Z4, S3)), implies(implies(S3, X4), implies(implies(V9, implies(W9, Z4)), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.56 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.99/9.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.57 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))))), true, ifeq(is_a_theorem(implies(implies(implies(V9, implies(W9, Z4)), implies(Z4, X4)), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8)))), implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.58 = { by axiom 2 (condensed_detachment) }
% 43.99/9.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.58 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.58 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T8, S8), implies(X9, Y9)), implies(implies(Y9, T8), implies(Z9, implies(X9, T8))))), true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.59 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.99/9.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.59 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.59 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4)))), implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(S3, X4), implies(X4, implies(implies(Y4, Z4), implies(Z4, X4))))), true, is_a_theorem(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.59 = { by axiom 2 (condensed_detachment) }
% 43.99/9.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.60 = { by axiom 1 (ifeq_axiom) }
% 43.99/9.60 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.60 = { by axiom 1 (ifeq_axiom) R->L }
% 43.99/9.60 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 43.99/9.60 = { by axiom 2 (condensed_detachment) R->L }
% 44.10/9.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.60 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.10/9.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.61 = { by axiom 1 (ifeq_axiom) }
% 44.10/9.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.61 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.62 = { by axiom 2 (condensed_detachment) R->L }
% 44.10/9.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.62 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.63 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.10/9.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.63 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.64 = { by axiom 2 (condensed_detachment) R->L }
% 44.10/9.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.64 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.65 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.10/9.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T9, implies(implies(S9, X10), implies(X10, T9))), implies(X10, U9)), implies(implies(U9, T9), implies(implies(Z11, implies(W11, X10)), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.66 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(implies(S9, X10), implies(X10, T9))), implies(X10, U9)), implies(implies(U9, T9), implies(implies(Z11, implies(W11, X10)), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.66 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.10/9.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T9, implies(implies(S9, X10), implies(X10, T9))), implies(X10, U9)), implies(implies(U9, T9), implies(implies(Z11, implies(W11, X10)), implies(X10, T9)))), implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))))), true, ifeq(is_a_theorem(implies(implies(implies(T9, implies(implies(S9, X10), implies(X10, T9))), implies(X10, U9)), implies(implies(U9, T9), implies(implies(Z11, implies(W11, X10)), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.67 = { by axiom 2 (condensed_detachment) }
% 44.10/9.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.68 = { by axiom 1 (ifeq_axiom) }
% 44.10/9.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.68 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.69 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.10/9.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, T9), implies(W11, S9)), implies(implies(S9, X10), implies(Z11, implies(W11, X10))))), true, is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.69 = { by axiom 1 (ifeq_axiom) R->L }
% 44.10/9.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X10, T9), implies(W11, S9)), implies(implies(S9, X10), implies(Z11, implies(W11, X10))))), true, is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.10/9.70 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.10/9.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, T9), implies(W11, S9)), implies(implies(S9, X10), implies(Z11, implies(W11, X10)))), implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true, ifeq(is_a_theorem(implies(implies(implies(X10, T9), implies(W11, S9)), implies(implies(S9, X10), implies(Z11, implies(W11, X10))))), true, is_a_theorem(implies(implies(implies(Z11, implies(W11, X10)), implies(X10, T9)), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.70 = { by axiom 2 (condensed_detachment) }
% 44.20/9.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.71 = { by axiom 1 (ifeq_axiom) }
% 44.20/9.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10)))), implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))))), true, ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(S10, X11)), implies(implies(X11, U10), implies(Y11, implies(S10, U10))))), true, is_a_theorem(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.71 = { by axiom 2 (condensed_detachment) }
% 44.20/9.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.72 = { by axiom 1 (ifeq_axiom) }
% 44.20/9.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.73 = { by axiom 1 (ifeq_axiom) R->L }
% 44.20/9.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.73 = { by axiom 2 (condensed_detachment) R->L }
% 44.20/9.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.75 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.20/9.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.75 = { by axiom 1 (ifeq_axiom) }
% 44.20/9.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.76 = { by axiom 1 (ifeq_axiom) R->L }
% 44.20/9.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.77 = { by axiom 2 (condensed_detachment) R->L }
% 44.20/9.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.79 = { by axiom 1 (ifeq_axiom) R->L }
% 44.20/9.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.20/9.80 = { by axiom 2 (condensed_detachment) R->L }
% 44.31/9.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))), implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, 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U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(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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% 44.31/9.81 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.31/9.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, 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% 44.31/9.82 = { by axiom 1 (ifeq_axiom) }
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% 44.31/9.84 = { by axiom 1 (ifeq_axiom) R->L }
% 44.31/9.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, 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% 44.31/9.85 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 44.31/9.87 = { by axiom 1 (ifeq_axiom) R->L }
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% 44.31/9.88 = { by axiom 2 (condensed_detachment) R->L }
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% 44.31/9.90 = { by axiom 1 (ifeq_axiom) R->L }
% 44.41/9.91 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(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true, 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% 44.41/9.92 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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% 44.41/9.94 = { by axiom 1 (ifeq_axiom) R->L }
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% 44.41/9.95 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
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implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.41/9.97 = { by axiom 2 (condensed_detachment) }
% 44.41/9.98 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(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, 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% 44.41/9.98 = { by axiom 1 (ifeq_axiom) }
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% 44.41/10.00 = { by axiom 1 (ifeq_axiom) R->L }
% 44.41/10.00 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(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, 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U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.41/10.01 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.41/10.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z12, implies(a, implies(b, a))), implies(Y13, Y12)), implies(implies(Y12, Z12), implies(X13, implies(Y13, Z12))))), true, is_a_theorem(implies(implies(implies(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, 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implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.41/10.02 = { by axiom 1 (ifeq_axiom) R->L }
% 44.41/10.03 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(Z12, implies(a, implies(b, a))), implies(Y13, Y12)), implies(implies(Y12, Z12), implies(X13, implies(Y13, Z12))))), true, is_a_theorem(implies(implies(implies(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, 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T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, 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implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.41/10.04 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.41/10.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z12, implies(a, implies(b, a))), implies(Y13, Y12)), implies(implies(Y12, Z12), implies(X13, implies(Y13, Z12)))), implies(implies(implies(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z12, implies(a, implies(b, a))), implies(Y13, Y12)), implies(implies(Y12, Z12), implies(X13, implies(Y13, Z12))))), true, is_a_theorem(implies(implies(implies(X13, implies(Y13, Z12)), implies(Z12, implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.41/10.05 = { by axiom 2 (condensed_detachment) }
% 44.41/10.06 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(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.58/10.06 = { by axiom 1 (ifeq_axiom) }
% 44.58/10.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.58/10.08 = { by axiom 2 (condensed_detachment) }
% 44.58/10.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, 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is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.58/10.09 = { by axiom 1 (ifeq_axiom) }
% 44.58/10.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.58/10.10 = { by axiom 1 (ifeq_axiom) R->L }
% 44.58/10.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), 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is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), 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% 44.58/10.12 = { by axiom 2 (condensed_detachment) R->L }
% 44.58/10.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(b, implies(a, implies(b, a)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), implies(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, 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% 44.58/10.13 = { by axiom 3 (ic_JLukasiewicz_5) }
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% 44.58/10.15 = { by axiom 1 (ifeq_axiom) }
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implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.68/10.16 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.68/10.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.68/10.17 = { by axiom 1 (ifeq_axiom) }
% 44.68/10.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y12, Z12), implies(Z12, implies(a, implies(b, a)))), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11)))), implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.68/10.19 = { by axiom 2 (condensed_detachment) }
% 44.68/10.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.68/10.20 = { by axiom 1 (ifeq_axiom) }
% 44.68/10.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V11, U11), implies(T11, S11)), implies(implies(S11, V11), implies(X12, implies(T11, V11))))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.21 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.73/10.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.21 = { by axiom 1 (ifeq_axiom) }
% 44.73/10.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.22 = { by axiom 1 (ifeq_axiom) R->L }
% 44.73/10.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.23 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.73/10.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(a, implies(b, a))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.24 = { by axiom 2 (condensed_detachment) }
% 44.73/10.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.24 = { by axiom 1 (ifeq_axiom) }
% 44.73/10.25 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.25 = { by axiom 1 (ifeq_axiom) R->L }
% 44.73/10.25 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.26 = { by axiom 2 (condensed_detachment) R->L }
% 44.73/10.26 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.27 = { by axiom 1 (ifeq_axiom) R->L }
% 44.73/10.27 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.28 = { by axiom 2 (condensed_detachment) R->L }
% 44.73/10.29 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), 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(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.29 = { by axiom 3 (ic_JLukasiewicz_5) }
% 44.73/10.30 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), 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(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.73/10.30 = { by axiom 1 (ifeq_axiom) }
% 44.83/10.31 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), 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(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.31 = { by axiom 1 (ifeq_axiom) R->L }
% 44.83/10.32 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), 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(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.33 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.83/10.33 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.34 = { by axiom 1 (ifeq_axiom) R->L }
% 44.83/10.34 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.35 = { by axiom 2 (condensed_detachment) R->L }
% 44.83/10.36 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), 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ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.37 = { by axiom 1 (ifeq_axiom) R->L }
% 44.83/10.37 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(Y14, Z14), 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ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.38 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.83/10.39 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(S13, X14), implies(X14, b))), implies(X14, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(implies(T14, implies(S14, X14)), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.83/10.39 = { by axiom 1 (ifeq_axiom) R->L }
% 44.83/10.40 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(S13, X14), implies(X14, b))), implies(X14, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(implies(T14, implies(S14, X14)), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.93/10.41 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.93/10.42 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, implies(implies(S13, X14), implies(X14, b))), implies(X14, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(implies(T14, implies(S14, X14)), implies(X14, b)))), implies(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(b, implies(implies(S13, X14), implies(X14, b))), implies(X14, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), 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implies(implies(S13, X14), implies(X14, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.93/10.43 = { by axiom 2 (condensed_detachment) }
% 44.93/10.44 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.93/10.45 = { by axiom 1 (ifeq_axiom) }
% 44.93/10.46 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.93/10.48 = { by axiom 1 (ifeq_axiom) R->L }
% 44.93/10.48 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 44.93/10.50 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 44.93/10.50 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X14, b), implies(S14, S13)), implies(implies(S13, X14), implies(T14, implies(S14, X14))))), true, is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.51 = { by axiom 1 (ifeq_axiom) R->L }
% 45.04/10.52 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X14, b), implies(S14, S13)), implies(implies(S13, X14), implies(T14, implies(S14, X14))))), true, is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.52 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.04/10.53 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X14, b), implies(S14, S13)), implies(implies(S13, X14), implies(T14, implies(S14, X14)))), implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(X14, b), implies(S14, S13)), implies(implies(S13, X14), implies(T14, implies(S14, X14))))), true, is_a_theorem(implies(implies(implies(T14, implies(S14, X14)), implies(X14, b)), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.53 = { by axiom 2 (condensed_detachment) }
% 45.04/10.54 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.54 = { by axiom 1 (ifeq_axiom) }
% 45.04/10.55 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), b), implies(b, implies(implies(S13, X14), implies(X14, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.56 = { by axiom 2 (condensed_detachment) }
% 45.04/10.56 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.57 = { by axiom 1 (ifeq_axiom) }
% 45.04/10.57 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.58 = { by axiom 1 (ifeq_axiom) R->L }
% 45.04/10.59 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.04/10.59 = { by axiom 2 (condensed_detachment) R->L }
% 45.04/10.60 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(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)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(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)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.61 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.14/10.62 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(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)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.62 = { by axiom 1 (ifeq_axiom) }
% 45.14/10.63 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), implies(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)))), implies(a, implies(b, a))))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.63 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.14/10.64 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.64 = { by axiom 1 (ifeq_axiom) }
% 45.14/10.66 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(X14, b)), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.66 = { by axiom 2 (condensed_detachment) }
% 45.14/10.66 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.66 = { by axiom 1 (ifeq_axiom) }
% 45.14/10.67 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.67 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.14/10.67 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, 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(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.67 = { by axiom 1 (ifeq_axiom) }
% 45.14/10.68 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)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), implies(a, implies(b, a))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(implies(U9, T9), implies(T9, implies(implies(S9, X10), implies(X10, T9)))), implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true), true), true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.68 = { by axiom 2 (condensed_detachment) }
% 45.14/10.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.68 = { by axiom 1 (ifeq_axiom) }
% 45.14/10.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.69 = { by axiom 1 (ifeq_axiom) R->L }
% 45.14/10.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.69 = { by axiom 2 (condensed_detachment) R->L }
% 45.14/10.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.69 = { by axiom 1 (ifeq_axiom) R->L }
% 45.14/10.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.14/10.70 = { by axiom 2 (condensed_detachment) R->L }
% 45.14/10.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V10, Z10), implies(U15, W10)), implies(implies(W10, V10), implies(T15, implies(U15, V10)))), implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true, ifeq(is_a_theorem(implies(implies(implies(V10, Z10), implies(U15, W10)), implies(implies(W10, V10), implies(T15, implies(U15, V10))))), true, is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.70 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V10, Z10), implies(U15, W10)), implies(implies(W10, V10), implies(T15, implies(U15, V10))))), true, is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.71 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V10, Z10), implies(U15, W10)), implies(implies(W10, V10), implies(T15, implies(U15, V10))))), true, is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.71 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.72 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.72 = { by axiom 1 (ifeq_axiom) R->L }
% 45.25/10.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.73 = { by axiom 2 (condensed_detachment) R->L }
% 45.25/10.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z10, implies(implies(W10, V10), implies(V10, Z10))), implies(V10, Y10)), implies(implies(Y10, Z10), implies(implies(T15, implies(U15, V10)), implies(V10, Z10)))), implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z10, implies(implies(W10, V10), implies(V10, Z10))), implies(V10, Y10)), implies(implies(Y10, Z10), implies(implies(T15, implies(U15, V10)), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.73 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z10, implies(implies(W10, V10), implies(V10, Z10))), implies(V10, Y10)), implies(implies(Y10, Z10), implies(implies(T15, implies(U15, V10)), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.74 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z10, implies(implies(W10, V10), implies(V10, Z10))), implies(V10, Y10)), implies(implies(Y10, Z10), implies(implies(T15, implies(U15, V10)), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.74 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.75 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))))), true, ifeq(is_a_theorem(implies(implies(implies(T15, implies(U15, V10)), implies(V10, Z10)), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15)))), implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.75 = { by axiom 2 (condensed_detachment) }
% 45.25/10.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.75 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X15, Y15), implies(Z15, W15)), implies(implies(W15, X15), implies(V15, implies(Z15, X15))))), true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.76 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.76 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10)))), implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(Y10, Z10), implies(Z10, implies(implies(W10, V10), implies(V10, Z10))))), true, is_a_theorem(implies(implies(a, implies(b, a)), implies(b, implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.76 = { by axiom 2 (condensed_detachment) }
% 45.25/10.76 ifeq(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(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.76 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.77 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(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 1 (ifeq_axiom) R->L }
% 45.25/10.77 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(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.25/10.77 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)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a))), implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))), a), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(b, a)))), true, is_a_theorem(implies(implies(implies(b, a), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))))), true), true), true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 2 (condensed_detachment) }
% 45.25/10.77 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 1 (ifeq_axiom) R->L }
% 45.25/10.77 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.77 = { by axiom 2 (condensed_detachment) R->L }
% 45.25/10.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.78 = { by axiom 1 (ifeq_axiom) R->L }
% 45.25/10.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.78 = { by axiom 2 (condensed_detachment) R->L }
% 45.25/10.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, X3), implies(V16, Y3)), implies(implies(Y3, Z3), implies(U16, implies(V16, Z3)))), implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(V16, Y3)), implies(implies(Y3, Z3), implies(U16, implies(V16, Z3))))), true, is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.78 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(V16, Y3)), implies(implies(Y3, Z3), implies(U16, implies(V16, Z3))))), true, is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.78 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.78 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z3, X3), implies(V16, Y3)), implies(implies(Y3, Z3), implies(U16, implies(V16, Z3))))), true, is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.79 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.79 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.79 = { by axiom 1 (ifeq_axiom) R->L }
% 45.25/10.79 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.79 = { by axiom 2 (condensed_detachment) R->L }
% 45.25/10.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(U16, implies(V16, Z3)), implies(Z3, X3)))), implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), 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(U16, implies(V16, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.80 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.25/10.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(U16, implies(V16, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.80 = { by axiom 1 (ifeq_axiom) }
% 45.25/10.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(U16, implies(V16, Z3)), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.25/10.80 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.80 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.80 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))))), true, ifeq(is_a_theorem(implies(implies(implies(U16, implies(V16, Z3)), implies(Z3, X3)), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(implies(S15, X16), implies(Y16, Z16)), implies(implies(Z16, S15), implies(W16, implies(Y16, S15)))), implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))))), true), 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 2 (condensed_detachment) }
% 45.35/10.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, 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(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), 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(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), 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(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3)))), implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(S2, X3), implies(X3, implies(implies(Y3, Z3), implies(Z3, X3))))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(implies(Z, W), implies(W, Y)))), implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 2 (condensed_detachment) }
% 45.35/10.81 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.81 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, is_a_theorem(implies(a, implies(b, a))), true)
% 45.35/10.81 = { by axiom 1 (ifeq_axiom) R->L }
% 45.35/10.81 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.81 = { by axiom 2 (condensed_detachment) R->L }
% 45.35/10.81 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.81 = { by axiom 1 (ifeq_axiom) R->L }
% 45.35/10.81 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.81 = { by axiom 2 (condensed_detachment) R->L }
% 45.35/10.81 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, U), implies(W17, T)), implies(implies(T, S), implies(V17, implies(W17, S)))), implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))))), true, ifeq(is_a_theorem(implies(implies(implies(S, U), implies(W17, T)), implies(implies(T, S), implies(V17, implies(W17, S))))), true, is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.81 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S, U), implies(W17, T)), implies(implies(T, S), implies(V17, implies(W17, S))))), true, is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, U), implies(W17, T)), implies(implies(T, S), implies(V17, implies(W17, S))))), true, is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 1 (ifeq_axiom) R->L }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 2 (condensed_detachment) R->L }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), 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(V17, implies(W17, S)), implies(S, U)))), implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), 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(V17, implies(W17, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.82 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), 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(V17, implies(W17, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.82 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), 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(V17, implies(W17, S)), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.83 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.83 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U))))))), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, S)), implies(S, U)), implies(U, implies(implies(T, S), implies(S, U))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(implies(Y17, T16), implies(Z17, implies(X17, T16)))), implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))))), 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.83 = { by axiom 2 (condensed_detachment) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.83 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), true, 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(V, U), implies(U, implies(implies(T, S), implies(S, U))))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 45.35/10.83 = { by axiom 3 (ic_JLukasiewicz_5) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), 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(b, a))), true), true)
% 45.35/10.83 = { by axiom 1 (ifeq_axiom) }
% 45.35/10.83 ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(implies(T, S), implies(S, U)))), implies(a, implies(b, a)))), 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(b, a))), true), true)
% 45.35/10.83 = { by axiom 2 (condensed_detachment) }
% 45.35/10.83 true
% 45.35/10.83 % SZS output end Proof
% 45.35/10.83
% 45.35/10.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------