%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:00 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.54s
% Output : Proof 5.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL087-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n002.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun Sep 27 15:23:51 UTC 2026
% 0.17/0.38 % CPUTime :
% 0.17/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.54 Command-line arguments: --no-flatten-goal
% 0.23/0.54
% 0.23/0.54 % SZS status Unsatisfiable
% 0.23/0.54
% 3.43/1.00 % SZS output start Proof
% 3.43/1.00 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.43/1.00 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.
% 3.43/1.02 Axiom 3 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 3.43/1.02
% 3.43/1.02 Goal 1 (prove_ic_2): is_a_theorem(implies(a, implies(b, a))) = true.
% 3.43/1.02 Proof:
% 3.43/1.02 is_a_theorem(implies(a, implies(b, a)))
% 3.43/1.02 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.02 ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.02 = { by axiom 2 (condensed_detachment) R->L }
% 3.43/1.02 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.02 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.02 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.02 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 3.43/1.02 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.03 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.03 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.03 = { by axiom 2 (condensed_detachment) R->L }
% 3.43/1.03 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(b, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(b, a), a), implies(b, a)))), implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(b, a), a), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.03 = { by axiom 3 (ic_JLukasiewicz_4) }
% 3.43/1.03 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(b, a), a), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 1 (ifeq_axiom) }
% 3.43/1.04 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(b, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(implies(implies(b, a), a), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 3 (ic_JLukasiewicz_4) }
% 3.43/1.04 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 1 (ifeq_axiom) }
% 3.43/1.04 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z)))), implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(V, U)), implies(T, implies(implies(U, Z), implies(V, Z))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 2 (condensed_detachment) }
% 3.43/1.04 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 1 (ifeq_axiom) }
% 3.43/1.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.04 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 2 (condensed_detachment) R->L }
% 3.43/1.04 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))), implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.04 = { by axiom 3 (ic_JLukasiewicz_4) }
% 3.43/1.04 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.05 = { by axiom 1 (ifeq_axiom) }
% 3.43/1.05 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.05 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.05 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.05 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 3.43/1.05 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.05 = { by axiom 1 (ifeq_axiom) R->L }
% 3.43/1.06 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.06 = { by axiom 2 (condensed_detachment) R->L }
% 3.43/1.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 3.43/1.06 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.07 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 4.69/1.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.08 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.08 = { by axiom 2 (condensed_detachment) R->L }
% 4.69/1.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))), implies(a, implies(T2, a))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))))), implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))), implies(a, implies(T2, a))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.09 = { by axiom 3 (ic_JLukasiewicz_4) }
% 4.69/1.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))), implies(a, implies(T2, a))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.10 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))), implies(a, implies(T2, a))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a)))))), true, is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.11 = { by axiom 3 (ic_JLukasiewicz_4) }
% 4.69/1.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.11 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2)))), implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(S2, X3), implies(Y3, Z3)), implies(W3, implies(implies(Z3, S2), implies(Y3, S2))))), true, is_a_theorem(implies(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.12 = { by axiom 2 (condensed_detachment) }
% 4.69/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.12 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.13 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 4.69/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.14 = { by axiom 2 (condensed_detachment) R->L }
% 4.69/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(b, a), a)), implies(implies(b, a), T2)), implies(implies(implies(b, a), a), implies(implies(T2, a), implies(implies(b, a), a)))), implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(b, a), a)), implies(implies(b, a), T2)), implies(implies(implies(b, a), a), implies(implies(T2, a), implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.14 = { by axiom 3 (ic_JLukasiewicz_4) }
% 4.69/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(b, a), a)), implies(implies(b, a), T2)), implies(implies(implies(b, a), a), implies(implies(T2, a), implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.14 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(b, a), a)), implies(implies(b, a), T2)), implies(implies(implies(b, a), a), implies(implies(T2, a), implies(implies(b, a), a))))), true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.15 = { by axiom 3 (ic_JLukasiewicz_4) }
% 4.69/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3)))), implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(V3, U3), implies(T3, S3)), implies(X4, implies(implies(S3, V3), implies(T3, V3))))), true, is_a_theorem(implies(implies(implies(implies(T2, a), implies(implies(b, a), a)), implies(a, implies(implies(b, a), a))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.15 = { by axiom 2 (condensed_detachment) }
% 4.69/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2)))), implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), implies(W2, V2)), implies(U2, implies(implies(V2, Y2), implies(W2, Y2))))), true, is_a_theorem(implies(implies(implies(b, a), a), implies(a, implies(implies(b, a), a)))), true), true), true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.15 = { by axiom 2 (condensed_detachment) }
% 4.69/1.16 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.16 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.16 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.16 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.16 = { by axiom 2 (condensed_detachment) R->L }
% 4.69/1.16 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.16 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.17 = { by axiom 2 (condensed_detachment) R->L }
% 4.69/1.17 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.17 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.17 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.17 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 4.69/1.18 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, implies(S, X2)), implies(S, W5)), implies(implies(S, X2), implies(implies(W5, X2), implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.18 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.18 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(S, X2)), implies(S, W5)), implies(implies(S, X2), implies(implies(W5, X2), implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.18 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 4.69/1.18 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, implies(S, X2)), implies(S, W5)), implies(implies(S, X2), implies(implies(W5, X2), implies(S, X2)))), implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(S, X2)), implies(S, W5)), implies(implies(S, X2), implies(implies(W5, X2), implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4)))), implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.18 = { by axiom 2 (condensed_detachment) }
% 4.69/1.19 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.19 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T4, S4), implies(X5, Y5)), implies(Z5, implies(implies(Y5, T4), implies(X5, T4))))), true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.19 = { by axiom 3 (ic_JLukasiewicz_4) }
% 4.69/1.19 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.69/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 4.69/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 4.69/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.20 = { by axiom 2 (condensed_detachment) R->L }
% 5.21/1.20 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.21/1.21 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.22 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.21/1.22 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(X2, implies(W5, X2))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2)))))), true, is_a_theorem(implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.22 = { by axiom 1 (ifeq_axiom) R->L }
% 5.21/1.22 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(X2, implies(W5, X2))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2)))))), true, is_a_theorem(implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.22 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.21/1.23 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(X2, implies(W5, X2))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))))), implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(X2, implies(W5, X2))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2)))))), true, is_a_theorem(implies(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5)))), implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.23 = { by axiom 2 (condensed_detachment) }
% 5.21/1.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.21/1.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V5, U5), implies(T5, S5)), implies(X6, implies(implies(S5, V5), implies(T5, V5))))), true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.24 = { by axiom 3 (ic_JLukasiewicz_4) }
% 5.21/1.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.21/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.21/1.24 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W5, X2), implies(S, X2)), implies(X2, implies(S, X2))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4)))), implies(implies(S, X2), implies(X2, implies(S, X2))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 2 (condensed_detachment) }
% 5.49/1.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(U4, implies(implies(V4, Y4), implies(W4, Y4))))), true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 3 (ic_JLukasiewicz_4) }
% 5.49/1.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(X2, implies(S, X2))), implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(S, X2), implies(X2, implies(S, X2)))), true, is_a_theorem(implies(implies(implies(implies(b, a), a), implies(b, a)), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 2 (condensed_detachment) }
% 5.49/1.25 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.25 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, is_a_theorem(implies(a, implies(b, a))), true)
% 5.49/1.25 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.25 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.25 = { by axiom 2 (condensed_detachment) R->L }
% 5.49/1.25 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.25 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.25 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.26 = { by axiom 2 (condensed_detachment) R->L }
% 5.49/1.26 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.26 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.26 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.26 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.49/1.26 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, W7)), implies(implies(X, Y), implies(implies(W7, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.26 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.26 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, W7)), implies(implies(X, Y), implies(implies(W7, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.26 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(X, Y)), implies(X, W7)), implies(implies(X, Y), implies(implies(W7, Y), implies(X, Y)))), implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(X, Y)), implies(X, W7)), implies(implies(X, Y), implies(implies(W7, Y), implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6)))), implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.27 = { by axiom 2 (condensed_detachment) }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.27 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T6, S6), implies(X7, Y7)), implies(Z7, implies(implies(Y7, T6), implies(X7, T6))))), true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.27 = { by axiom 3 (ic_JLukasiewicz_4) }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.27 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.27 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.27 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.28 = { by axiom 2 (condensed_detachment) R->L }
% 5.49/1.28 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.28 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.28 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.28 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.49/1.29 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(W7, Y))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.29 = { by axiom 1 (ifeq_axiom) R->L }
% 5.49/1.29 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(W7, Y))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.29 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 5.49/1.29 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(W7, Y))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))))), implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(Y, implies(W7, Y))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y)))))), true, is_a_theorem(implies(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7)))), implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.29 = { by axiom 2 (condensed_detachment) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V7, U7), implies(T7, S7)), implies(X8, implies(implies(S7, V7), implies(T7, V7))))), true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 3 (ic_JLukasiewicz_4) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y)))), implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W7, Y), implies(X, Y)), implies(Y, implies(X, Y))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6)))), implies(implies(X, Y), implies(Y, implies(X, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 2 (condensed_detachment) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y6, Z6), implies(W6, V6)), implies(U6, implies(implies(V6, Y6), implies(W6, Y6))))), true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 3 (ic_JLukasiewicz_4) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 1 (ifeq_axiom) }
% 5.49/1.30 ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Y, implies(X, Y))), implies(a, implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(X, Y), implies(Y, implies(X, Y)))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 5.49/1.30 = { by axiom 2 (condensed_detachment) }
% 5.49/1.30 true
% 5.49/1.30 % SZS output end Proof
% 5.49/1.30
% 5.49/1.30 RESULT: Unsatisfiable (the axioms are contradictory).
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