%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL090-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:00 AM UTC 2026
% Result : Unsatisfiable 1.38s 0.65s
% Output : Proof 50.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL090-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 15:23:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.38/0.65 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.38/0.65
% 1.38/0.65 % SZS status Unsatisfiable
% 1.38/0.65
% 37.75/5.96 % SZS output start Proof
% 37.75/5.96 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 37.75/5.96 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.
% 39.12/6.10 Axiom 3 (ic_JLukasiewicz_5): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))) = true.
% 39.12/6.10
% 39.12/6.10 Goal 1 (prove_ic_1): is_a_theorem(implies(a, a)) = true.
% 39.12/6.10 Proof:
% 39.12/6.10 is_a_theorem(implies(a, a))
% 39.12/6.10 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.10 ifeq(true, true, is_a_theorem(implies(a, a)), true)
% 39.12/6.10 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.10 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.10 = { by axiom 2 (condensed_detachment) R->L }
% 39.12/6.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X))))), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.12/6.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 1 (ifeq_axiom) }
% 39.12/6.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.11 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 2 (condensed_detachment) R->L }
% 39.12/6.11 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S))))), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.12/6.11 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.11 = { by axiom 1 (ifeq_axiom) }
% 39.12/6.11 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.12 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.12 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.12 = { by axiom 2 (condensed_detachment) R->L }
% 39.12/6.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.12 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.12/6.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.13 = { by axiom 1 (ifeq_axiom) }
% 39.12/6.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.14 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.14 = { by axiom 2 (condensed_detachment) R->L }
% 39.12/6.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a)))), implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.15 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.12/6.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.16 = { by axiom 1 (ifeq_axiom) }
% 39.12/6.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.17 = { by axiom 1 (ifeq_axiom) R->L }
% 39.12/6.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.18 = { by axiom 2 (condensed_detachment) R->L }
% 39.12/6.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.12/6.20 = { by axiom 1 (ifeq_axiom) R->L }
% 39.87/6.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.21 = { by axiom 2 (condensed_detachment) R->L }
% 39.87/6.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4))))), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.23 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.87/6.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.24 = { by axiom 1 (ifeq_axiom) }
% 39.87/6.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.26 = { by axiom 1 (ifeq_axiom) R->L }
% 39.87/6.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.28 = { by axiom 2 (condensed_detachment) R->L }
% 39.87/6.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(T4, V2)), implies(implies(V2, a), implies(S4, implies(T4, a)))), implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(T4, V2)), implies(implies(V2, a), implies(S4, implies(T4, a))))), true, is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 39.87/6.29 = { by axiom 3 (ic_JLukasiewicz_5) }
% 39.87/6.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(T4, V2)), implies(implies(V2, a), implies(S4, implies(T4, a)))), implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.31 = { by axiom 1 (ifeq_axiom) }
% 40.55/6.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(T4, V2)), implies(implies(V2, a), implies(S4, implies(T4, a)))), implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.32 = { by axiom 3 (ic_JLukasiewicz_5) }
% 40.55/6.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.34 = { by axiom 1 (ifeq_axiom) }
% 40.55/6.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.36 = { by axiom 1 (ifeq_axiom) R->L }
% 40.55/6.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.37 = { by axiom 2 (condensed_detachment) R->L }
% 40.55/6.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(S4, implies(T4, a)), implies(a, a)))), implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(S4, implies(T4, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 40.55/6.39 = { by axiom 3 (ic_JLukasiewicz_5) }
% 35.75/6.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(S4, implies(T4, a)), implies(a, a)))), implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.41 = { by axiom 1 (ifeq_axiom) }
% 35.75/6.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(S4, implies(T4, a)), implies(a, a)))), implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))))), true, is_a_theorem(implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.43 = { by axiom 3 (ic_JLukasiewicz_5) }
% 35.75/6.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.45 = { by axiom 1 (ifeq_axiom) }
% 35.75/6.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(S4, implies(T4, a)), implies(a, a)), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y4, Z4), implies(W4, V4)), implies(implies(V4, Y4), implies(U4, implies(W4, Y4)))), implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.46 = { by axiom 2 (condensed_detachment) }
% 35.75/6.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.47 = { by axiom 1 (ifeq_axiom) }
% 35.75/6.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.48 = { by axiom 1 (ifeq_axiom) R->L }
% 35.75/6.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.49 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 35.75/6.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.51 = { by axiom 2 (condensed_detachment) }
% 35.75/6.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.51 = { by axiom 1 (ifeq_axiom) }
% 35.75/6.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V2, a), implies(a, a)), a), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.52 = { by axiom 3 (ic_JLukasiewicz_5) }
% 35.75/6.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.53 = { by axiom 1 (ifeq_axiom) }
% 35.75/6.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.54 = { by axiom 1 (ifeq_axiom) R->L }
% 35.75/6.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.55 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 35.75/6.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(V2, a), implies(a, a))), implies(implies(S3, implies(X4, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(S3, implies(X4, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 35.75/6.56 = { by axiom 2 (condensed_detachment) }
% 35.75/6.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.57 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.57 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.58 = { by axiom 2 (condensed_detachment) R->L }
% 42.35/6.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(X4, V2)), implies(implies(V2, a), implies(S3, implies(X4, a)))), implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(X4, V2)), implies(implies(V2, a), implies(S3, implies(X4, a))))), true, is_a_theorem(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.59 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.35/6.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(X4, V2)), implies(implies(V2, a), implies(S3, implies(X4, a)))), implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.60 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(X4, V2)), implies(implies(V2, a), implies(S3, implies(X4, a)))), implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.61 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.35/6.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.62 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(S3, implies(X4, a)), implies(a, a)), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), implies(S2, X3)), implies(implies(X3, U2), implies(Y3, implies(S2, U2)))), implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.62 = { by axiom 2 (condensed_detachment) }
% 42.35/6.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 42.35/6.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3)))), implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(Z3, W3), implies(V3, U3)), implies(implies(U3, Z3), implies(T3, implies(V3, Z3))))), true, is_a_theorem(implies(implies(implies(implies(S, X2), implies(Y2, Z2)), implies(implies(Z2, S), implies(W2, implies(Y2, S)))), implies(implies(V2, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 2 (condensed_detachment) }
% 42.35/6.63 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(V2, a), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.63 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.63 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.64 = { by axiom 2 (condensed_detachment) R->L }
% 42.35/6.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a))), implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.64 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.35/6.64 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.64 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.64 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.65 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.65 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.65 = { by axiom 2 (condensed_detachment) R->L }
% 42.35/6.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(a, a)), implies(implies(a, a), implies(V2, implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.65 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.35/6.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.65 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(a, a))), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.66 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.66 = { by axiom 2 (condensed_detachment) R->L }
% 42.35/6.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.67 = { by axiom 3 (ic_JLukasiewicz_5) }
% 42.35/6.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.68 = { by axiom 1 (ifeq_axiom) }
% 42.35/6.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.68 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.69 = { by axiom 2 (condensed_detachment) R->L }
% 42.35/6.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 42.35/6.71 = { by axiom 1 (ifeq_axiom) R->L }
% 42.35/6.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.27/6.72 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.27/6.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(W6, a)), implies(implies(a, a), implies(Z6, implies(W6, a)))), implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.27/6.73 = { by axiom 1 (ifeq_axiom) R->L }
% 43.27/6.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(W6, a)), implies(implies(a, a), implies(Z6, implies(W6, a)))), implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.27/6.74 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.27/6.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(W6, a)), implies(implies(a, a), implies(Z6, implies(W6, a)))), implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(W6, a)), implies(implies(a, a), implies(Z6, implies(W6, a))))), true, is_a_theorem(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.27/6.75 = { by axiom 2 (condensed_detachment) }
% 43.27/6.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.57/6.76 = { by axiom 1 (ifeq_axiom) }
% 43.57/6.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.57/6.77 = { by axiom 1 (ifeq_axiom) R->L }
% 43.57/6.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.57/6.78 = { by axiom 2 (condensed_detachment) R->L }
% 43.57/6.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.57/6.79 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.82/6.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.81 = { by axiom 1 (ifeq_axiom) }
% 43.82/6.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.83 = { by axiom 1 (ifeq_axiom) R->L }
% 43.82/6.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.84 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 43.82/6.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.86 = { by axiom 1 (ifeq_axiom) R->L }
% 43.82/6.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.87 = { by axiom 2 (condensed_detachment) R->L }
% 43.82/6.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 43.82/6.89 = { by axiom 3 (ic_JLukasiewicz_5) }
% 43.82/6.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 44.42/6.91 = { by axiom 1 (ifeq_axiom) }
% 44.42/6.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 44.42/6.93 = { by axiom 1 (ifeq_axiom) R->L }
% 44.42/6.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 44.42/6.95 = { by axiom 2 (condensed_detachment) R->L }
% 44.42/6.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 44.42/6.98 = { by axiom 1 (ifeq_axiom) R->L }
% 44.42/6.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 44.42/7.00 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.01/7.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(Y7, implies(Z7, a)), implies(a, a)))), implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))))), true, is_a_theorem(implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), 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implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), 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% 45.01/7.02 = { by axiom 1 (ifeq_axiom) R->L }
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implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), 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implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.01/7.04 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.01/7.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(Y7, implies(Z7, a)), implies(a, a)))), implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(a, a), implies(implies(Y7, implies(Z7, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.01/7.09 = { by axiom 2 (condensed_detachment) }
% 45.01/7.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.01/7.10 = { by axiom 1 (ifeq_axiom) }
% 45.62/7.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.11 = { by axiom 1 (ifeq_axiom) R->L }
% 45.62/7.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.12 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.62/7.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(Z7, a)), implies(implies(a, a), implies(Y7, implies(Z7, a)))), implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.13 = { by axiom 1 (ifeq_axiom) R->L }
% 45.62/7.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(Z7, a)), implies(implies(a, a), implies(Y7, implies(Z7, a)))), implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.14 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.62/7.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(Z7, a)), implies(implies(a, a), implies(Y7, implies(Z7, a)))), implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(Z7, a)), implies(implies(a, a), implies(Y7, implies(Z7, a))))), true, is_a_theorem(implies(implies(implies(Y7, implies(Z7, a)), implies(a, a)), implies(a, implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.15 = { by axiom 2 (condensed_detachment) }
% 45.62/7.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.16 = { by axiom 1 (ifeq_axiom) }
% 45.62/7.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.17 = { by axiom 1 (ifeq_axiom) R->L }
% 45.62/7.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.18 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 45.62/7.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7)))), implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(W7, V7), implies(U7, T7)), implies(implies(T7, W7), implies(S7, implies(U7, W7))))), true, is_a_theorem(implies(implies(a, a), implies(a, implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.19 = { by axiom 2 (condensed_detachment) }
% 45.62/7.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 45.62/7.20 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a))), implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(a, a)), a), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(a, a), implies(implies(a, a), implies(a, a))), implies(implies(Z6, implies(W6, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.20 = { by axiom 2 (condensed_detachment) }
% 46.23/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.21 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.21 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.22 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 46.23/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a)))), implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))), implies(a, a)), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(Z6, implies(W6, a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Z6, implies(W6, a)), implies(a, a)), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.23 = { by axiom 2 (condensed_detachment) }
% 46.23/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.23 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.23 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.23 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6)))), implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(V6, U6), implies(T6, S6)), implies(implies(S6, V6), implies(X7, implies(T6, V6))))), true, is_a_theorem(implies(implies(implies(implies(X5, Y5), implies(Z5, W5)), implies(implies(W5, X5), implies(V5, implies(Z5, X5)))), implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 2 (condensed_detachment) }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5)))), implies(implies(a, a), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(U5, T5), implies(S5, X6)), implies(implies(X6, U5), implies(Y6, implies(S5, U5))))), true, is_a_theorem(implies(implies(a, a), implies(a, a))), true), true), true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 2 (condensed_detachment) }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(V2, implies(a, a))), implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(V2, implies(a, a)))), true, is_a_theorem(implies(implies(implies(a, a), a), implies(implies(U, implies(T, T)), implies(V2, a)))), true), true), true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.24 = { by axiom 2 (condensed_detachment) }
% 46.23/7.24 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.25 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V2, a), implies(a, a)), implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(V2, a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, Y), implies(Z, W)), implies(implies(W, X), implies(V, implies(Z, X)))), implies(implies(U, implies(T, T)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 2 (condensed_detachment) }
% 46.23/7.25 ifeq(ifeq(true, true, is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true, ifeq(is_a_theorem(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8))))), true, is_a_theorem(implies(U, implies(T, T))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true, ifeq(true, true, is_a_theorem(implies(U, implies(T, T))), true), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8))))), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true, ifeq(true, true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.25 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.25 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.26 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.26 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.26 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.26 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.23/7.26 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.26 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.26 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.26 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.27 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.27 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.27 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T)))), implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.27 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.23/7.28 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.28 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.28 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.29 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.29 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.29 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.29 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.23/7.30 = { by axiom 1 (ifeq_axiom) R->L }
% 46.82/7.30 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.31 = { by axiom 2 (condensed_detachment) R->L }
% 46.82/7.31 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10))))), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.31 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.82/7.32 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.32 = { by axiom 1 (ifeq_axiom) }
% 46.82/7.33 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.33 = { by axiom 1 (ifeq_axiom) R->L }
% 46.82/7.34 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.34 = { by axiom 2 (condensed_detachment) R->L }
% 46.82/7.35 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(V11, Z9)), implies(implies(Z9, T), implies(U11, implies(V11, T)))), implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(V11, Z9)), implies(implies(Z9, T), implies(U11, implies(V11, T))))), true, is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.35 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.82/7.35 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(V11, Z9)), implies(implies(Z9, T), implies(U11, implies(V11, T)))), implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.36 = { by axiom 1 (ifeq_axiom) }
% 46.82/7.36 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(V11, Z9)), implies(implies(Z9, T), implies(U11, implies(V11, T)))), implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.37 = { by axiom 3 (ic_JLukasiewicz_5) }
% 46.82/7.37 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.38 = { by axiom 1 (ifeq_axiom) }
% 46.82/7.38 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.39 = { by axiom 1 (ifeq_axiom) R->L }
% 46.82/7.39 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 46.82/7.40 = { by axiom 2 (condensed_detachment) R->L }
% 47.43/7.41 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(U11, implies(V11, T)), implies(T, T)))), implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))))), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(U11, implies(V11, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.41 = { by axiom 3 (ic_JLukasiewicz_5) }
% 47.43/7.42 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(U11, implies(V11, T)), implies(T, T)))), implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.42 = { by axiom 1 (ifeq_axiom) }
% 47.43/7.42 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(U11, implies(V11, T)), implies(T, T)))), implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))))), true, is_a_theorem(implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.43 = { by axiom 3 (ic_JLukasiewicz_5) }
% 47.43/7.43 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.44 = { by axiom 1 (ifeq_axiom) }
% 47.43/7.44 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(U11, implies(V11, T)), implies(T, T)), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(implies(Z11, S10), implies(W11, implies(Y11, S10)))), implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.45 = { by axiom 2 (condensed_detachment) }
% 47.43/7.45 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.45 = { by axiom 1 (ifeq_axiom) }
% 47.43/7.46 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.46 = { by axiom 1 (ifeq_axiom) R->L }
% 47.43/7.46 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.47 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 47.43/7.47 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.47 = { by axiom 2 (condensed_detachment) }
% 47.43/7.48 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.48 = { by axiom 1 (ifeq_axiom) }
% 47.43/7.48 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, T), implies(T, T)), T), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.48 = { by axiom 3 (ic_JLukasiewicz_5) }
% 47.43/7.49 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.49 = { by axiom 1 (ifeq_axiom) }
% 47.43/7.49 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.49 = { by axiom 1 (ifeq_axiom) R->L }
% 47.43/7.49 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 47.43/7.50 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 48.04/7.50 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(Z9, T), implies(T, T))), implies(implies(U10, implies(T10, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(U10, implies(T10, T)), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.50 = { by axiom 2 (condensed_detachment) }
% 48.04/7.50 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.51 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.51 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.51 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.51 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.52 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.52 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(T10, Z9)), implies(implies(Z9, T), implies(U10, implies(T10, T)))), implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(T10, Z9)), implies(implies(Z9, T), implies(U10, implies(T10, T))))), true, is_a_theorem(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.52 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.52 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(T10, Z9)), implies(implies(Z9, T), implies(U10, implies(T10, T)))), implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.52 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.53 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(T10, Z9)), implies(implies(Z9, T), implies(U10, implies(T10, T)))), implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.53 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.53 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.53 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.53 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(U10, implies(T10, T)), implies(T, T)), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(implies(T9, W9), implies(S9, implies(U9, W9)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 2 (condensed_detachment) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(implies(W10, X10), implies(V10, implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(implies(X9, U8), implies(Y9, implies(S8, U8)))), implies(implies(Z9, T), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 2 (condensed_detachment) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z9, T), implies(T, T))), true), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), T), implies(U, implies(Z9, T))), implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.54 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.54 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(T, T)), implies(implies(T, T), implies(Z9, implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, T))), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, T))), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, T), implies(T, T))), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.55 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11))))), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.55 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.56 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.56 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.56 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.56 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.57 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.57 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.57 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.58 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.58 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.58 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 48.04/7.58 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(Y13, T)), implies(implies(T, T), implies(X13, implies(Y13, T)))), implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.59 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.59 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(Y13, T)), implies(implies(T, T), implies(X13, implies(Y13, T)))), implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.59 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 48.04/7.60 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(Y13, T)), implies(implies(T, T), implies(X13, implies(Y13, T)))), implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(Y13, T)), implies(implies(T, T), implies(X13, implies(Y13, T))))), true, is_a_theorem(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.61 = { by axiom 2 (condensed_detachment) }
% 48.04/7.61 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.61 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.61 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.62 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.62 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.62 = { by axiom 2 (condensed_detachment) R->L }
% 48.04/7.62 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.63 = { by axiom 3 (ic_JLukasiewicz_5) }
% 48.04/7.63 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.63 = { by axiom 1 (ifeq_axiom) }
% 48.04/7.64 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.64 = { by axiom 1 (ifeq_axiom) R->L }
% 48.04/7.64 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.65 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 48.04/7.65 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 48.04/7.65 = { by axiom 1 (ifeq_axiom) R->L }
% 49.00/7.66 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.66 = { by axiom 2 (condensed_detachment) R->L }
% 49.00/7.67 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.67 = { by axiom 3 (ic_JLukasiewicz_5) }
% 49.00/7.68 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.68 = { by axiom 1 (ifeq_axiom) }
% 49.00/7.69 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.69 = { by axiom 1 (ifeq_axiom) R->L }
% 49.00/7.70 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.71 = { by axiom 2 (condensed_detachment) R->L }
% 49.00/7.71 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.72 = { by axiom 1 (ifeq_axiom) R->L }
% 49.00/7.72 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.73 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.00/7.74 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(S13, implies(X14, T)), implies(T, T)))), implies(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))), 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% 49.00/7.74 = { by axiom 1 (ifeq_axiom) R->L }
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implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.00/7.75 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.54/7.76 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(S13, implies(X14, T)), implies(T, T)))), implies(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))))), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(T, T), implies(implies(S13, implies(X14, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.54/7.77 = { by axiom 2 (condensed_detachment) }
% 49.54/7.77 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.54/7.78 = { by axiom 1 (ifeq_axiom) }
% 49.54/7.78 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.54/7.79 = { by axiom 1 (ifeq_axiom) R->L }
% 49.54/7.79 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.54/7.80 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.75/7.80 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(X14, T)), implies(implies(T, T), implies(S13, implies(X14, T)))), implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.81 = { by axiom 1 (ifeq_axiom) R->L }
% 49.75/7.82 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(X14, T)), implies(implies(T, T), implies(S13, implies(X14, T)))), implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.82 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.75/7.83 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(X14, T)), implies(implies(T, T), implies(S13, implies(X14, T)))), implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(T, T), implies(X14, T)), implies(implies(T, T), implies(S13, implies(X14, T))))), true, is_a_theorem(implies(implies(implies(S13, implies(X14, T)), implies(T, T)), implies(T, implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.83 = { by axiom 2 (condensed_detachment) }
% 49.75/7.84 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.84 = { by axiom 1 (ifeq_axiom) }
% 49.75/7.85 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.85 = { by axiom 1 (ifeq_axiom) R->L }
% 49.75/7.85 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.86 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.75/7.86 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14)))), implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y14, Z14), implies(W14, V14)), implies(implies(V14, Y14), implies(U14, implies(W14, Y14))))), true, is_a_theorem(implies(implies(T, T), implies(T, implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.86 = { by axiom 2 (condensed_detachment) }
% 49.75/7.87 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.87 = { by axiom 1 (ifeq_axiom) }
% 49.75/7.88 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T))), implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T, T), implies(T, T)), T), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(T, T)))), true, is_a_theorem(implies(implies(implies(T, T), implies(implies(T, T), implies(T, T))), implies(implies(X13, implies(Y13, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.88 = { by axiom 2 (condensed_detachment) }
% 49.75/7.88 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.88 = { by axiom 1 (ifeq_axiom) }
% 49.75/7.89 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.89 = { by axiom 1 (ifeq_axiom) R->L }
% 49.75/7.89 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.89 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 49.75/7.90 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T)))), implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))), implies(T, T)), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(X13, implies(Y13, T)), implies(T, T))))), true, is_a_theorem(implies(implies(implies(implies(X13, implies(Y13, T)), implies(T, T)), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 49.75/7.90 = { by axiom 2 (condensed_detachment) }
% 49.75/7.90 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.90 = { by axiom 1 (ifeq_axiom) }
% 50.27/7.90 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.90 = { by axiom 1 (ifeq_axiom) R->L }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13)))), implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z13, W13), implies(V13, U13)), implies(implies(U13, Z13), implies(T13, implies(V13, Z13))))), true, is_a_theorem(implies(implies(implies(implies(T11, S11), implies(X12, Y12)), implies(implies(Y12, T11), implies(Z12, implies(X12, T11)))), implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 2 (condensed_detachment) }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 1 (ifeq_axiom) }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 1 (ifeq_axiom) R->L }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true, ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12)))), implies(implies(T, T), implies(T, T)))), true, ifeq(is_a_theorem(implies(implies(implies(W12, V12), implies(U12, T12)), implies(implies(T12, W12), implies(S12, implies(U12, W12))))), true, is_a_theorem(implies(implies(T, T), implies(T, T))), true), true), true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 2 (condensed_detachment) }
% 50.27/7.91 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.91 = { by axiom 1 (ifeq_axiom) }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 1 (ifeq_axiom) R->L }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 3 (ic_JLukasiewicz_5) R->L }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T, T), implies(Z9, implies(T, T))), implies(implies(implies(T, T), T), implies(U, implies(Z9, T))))), true, ifeq(is_a_theorem(implies(implies(T, T), implies(Z9, implies(T, T)))), true, is_a_theorem(implies(implies(implies(T, T), T), implies(U, implies(Z9, T)))), true), true), true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 2 (condensed_detachment) }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 1 (ifeq_axiom) }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z9, T), implies(T, T)), implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T))))), true, ifeq(is_a_theorem(implies(implies(Z9, T), implies(T, T))), true, is_a_theorem(implies(implies(implies(implies(X8, Y8), implies(Z8, W8)), implies(implies(W8, X8), implies(V8, implies(Z8, X8)))), implies(U, implies(T, T)))), true), true), true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 2 (condensed_detachment) }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(ifeq(true, true, is_a_theorem(implies(U, implies(T, T))), true), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 1 (ifeq_axiom) }
% 50.27/7.92 ifeq(is_a_theorem(implies(implies(U, implies(T, T)), implies(a, a))), true, ifeq(is_a_theorem(implies(U, implies(T, T))), true, is_a_theorem(implies(a, a)), true), true)
% 50.27/7.92 = { by axiom 2 (condensed_detachment) }
% 50.27/7.92 true
% 50.27/7.92 % SZS output end Proof
% 50.27/7.92
% 50.27/7.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------