%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL089-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 1.78s 0.67s
% Output : Proof 51.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL089-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 15:21:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.78/0.67 Command-line arguments: --no-flatten-goal
% 1.78/0.67
% 1.78/0.67 % SZS status Unsatisfiable
% 1.78/0.67
% 40.63/6.77 % SZS output start Proof
% 40.63/6.77 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 40.63/6.77 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.
% 41.14/6.89 Axiom 3 (ic_JLukasiewicz_4): is_a_theorem(implies(implies(implies(X, Y), implies(Z, W)), implies(V, implies(implies(W, X), implies(Z, X))))) = true.
% 41.14/6.89
% 41.14/6.89 Goal 1 (prove_ic_4): is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))) = true.
% 41.14/6.89 Proof:
% 41.14/6.89 is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c))))
% 41.14/6.89 = { by axiom 1 (ifeq_axiom) R->L }
% 41.14/6.89 ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 2 (condensed_detachment) R->L }
% 41.14/6.89 ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 1 (ifeq_axiom) R->L }
% 41.14/6.89 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 2 (condensed_detachment) R->L }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 1 (ifeq_axiom) }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 1 (ifeq_axiom) R->L }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 2 (condensed_detachment) R->L }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.89 = { by axiom 1 (ifeq_axiom) R->L }
% 41.14/6.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.90 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.14/6.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.90 = { by axiom 1 (ifeq_axiom) R->L }
% 41.14/6.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.14/6.90 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.90 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.90 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/6.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.91 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.91 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(U, implies(W2, U))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))))), implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(U, implies(W2, U))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U)))))), true, is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.91 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/6.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(U, implies(W2, U))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U)))))), true, is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.92 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(U, implies(W2, U))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U)))))), true, is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.92 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/6.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.92 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2)))), implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))))), true, ifeq(is_a_theorem(implies(implies(implies(V2, U2), implies(T2, S2)), implies(X3, implies(implies(S2, V2), implies(T2, V2))))), true, is_a_theorem(implies(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))), implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.92 = { by axiom 2 (condensed_detachment) }
% 41.64/6.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.93 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.93 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.93 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/6.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.93 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.94 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, implies(V, U)), implies(V, W2)), implies(implies(V, U), implies(implies(W2, U), implies(V, U)))), implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))))), true, ifeq(is_a_theorem(implies(implies(implies(U, implies(V, U)), implies(V, W2)), implies(implies(V, U), implies(implies(W2, U), implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.94 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/6.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U, implies(V, U)), implies(V, W2)), implies(implies(V, U), implies(implies(W2, U), implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.94 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U, implies(V, U)), implies(V, W2)), implies(implies(V, U), implies(implies(W2, U), implies(V, U))))), true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.94 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/6.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.94 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3)))), implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y3, Z3), implies(W3, V3)), implies(U3, implies(implies(V3, Y3), implies(W3, Y3))))), true, is_a_theorem(implies(implies(implies(implies(W2, U), implies(V, U)), implies(U, implies(V, U))), implies(implies(V, U), implies(U, implies(V, U))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 2 (condensed_detachment) }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T)))), implies(implies(V, U), implies(U, implies(V, U))))), true, ifeq(is_a_theorem(implies(implies(implies(T, S), implies(X2, Y2)), implies(Z2, implies(implies(Y2, T), implies(X2, T))))), true, is_a_theorem(implies(implies(V, U), implies(U, implies(V, U)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 2 (condensed_detachment) }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.95 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.96 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.96 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.96 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.97 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/6.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(implies(c, X), implies(a, b)), X5)), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.97 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(implies(c, X), implies(a, b)), X5)), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.97 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/6.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(implies(c, X), implies(a, b)), X5)), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(implies(c, X), implies(a, b)), X5)), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4)))), implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.97 = { by axiom 2 (condensed_detachment) }
% 41.64/6.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.98 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W4, V4), implies(U4, T4)), implies(S4, implies(implies(T4, W4), implies(U4, W4))))), true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.98 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/6.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.98 = { by axiom 1 (ifeq_axiom) }
% 41.64/6.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.99 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/6.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.99 = { by axiom 2 (condensed_detachment) R->L }
% 41.64/6.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/6.99 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/7.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.00 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/7.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(a, b), implies(X5, implies(a, b)))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.00 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/7.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(a, b), implies(X5, implies(a, b)))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.01 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/7.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(a, b), implies(X5, implies(a, b)))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(a, b), implies(X5, implies(a, b)))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true, is_a_theorem(implies(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5)))), implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.01 = { by axiom 2 (condensed_detachment) }
% 41.64/7.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.01 = { by axiom 1 (ifeq_axiom) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y5, Z5), implies(W5, V5)), implies(U5, implies(implies(V5, Y5), implies(W5, Y5))))), true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 1 (ifeq_axiom) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X5, implies(a, b)), implies(implies(implies(c, X), implies(a, b)), implies(a, b))), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3)))), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 2 (condensed_detachment) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 1 (ifeq_axiom) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T3, S3), implies(X4, Y4)), implies(Z4, implies(implies(Y4, T3), implies(X4, T3))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 3 (ic_JLukasiewicz_4) }
% 41.64/7.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.02 = { by axiom 1 (ifeq_axiom) }
% 41.64/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.03 = { by axiom 1 (ifeq_axiom) R->L }
% 41.64/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.03 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 41.64/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b)))), implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(a, b), implies(implies(implies(c, X), implies(a, b)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(V, U), implies(U, implies(V, U))), implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.03 = { by axiom 2 (condensed_detachment) }
% 41.64/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 41.64/7.03 = { by axiom 1 (ifeq_axiom) }
% 41.64/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.03 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.03 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.03 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(c, X), implies(a, b))), implies(implies(c, X), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(c, X), implies(a, b))), implies(implies(c, X), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(c, X), implies(a, b))), implies(implies(c, X), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))))), implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(c, X), implies(a, b))), implies(implies(c, X), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5)))), implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 2 (condensed_detachment) }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T5, S5), implies(X6, Y6)), implies(Z6, implies(implies(Y6, T5), implies(X6, T5))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.04 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.05 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b)))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(c, X), implies(a, b)), implies(a, b)), implies(implies(c, X), implies(a, b))), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), Y), implies(implies(a, b), implies(implies(c, X), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 2 (condensed_detachment) }
% 42.31/7.05 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.05 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.05 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W)))), implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true, ifeq(is_a_theorem(implies(implies(implies(W, implies(Z, W)), implies(Z, U7)), implies(implies(Z, W), implies(implies(U7, W), implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7)))), implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 2 (condensed_detachment) }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X7, Y7), implies(Z7, W7)), implies(V7, implies(implies(W7, X7), implies(Z7, X7))))), true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.06 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.06 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.07 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.07 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.07 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.07 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.07 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.07 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.07 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.07 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.07 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))))), implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(W, implies(U7, W))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W)))))), true, is_a_theorem(implies(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7)))), implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 2 (condensed_detachment) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T7, S7), implies(X8, Y8)), implies(Z8, implies(implies(Y8, T7), implies(X8, T7))))), true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W)))), implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U7, W), implies(Z, W)), implies(W, implies(Z, W))), implies(implies(Z, W), implies(W, implies(Z, W))))), true, is_a_theorem(implies(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6)))), implies(implies(Z, W), implies(W, implies(Z, W))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 2 (condensed_detachment) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W6, V6), implies(U6, T6)), implies(S6, implies(implies(T6, W6), implies(U6, W6))))), true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.08 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, W), implies(W, implies(Z, W))), implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(Z, W), implies(W, implies(Z, W)))), true, is_a_theorem(implies(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.08 = { by axiom 2 (condensed_detachment) }
% 42.31/7.09 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(c, X), implies(a, b)), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.09 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.09 ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.09 ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.09 ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.09 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.09 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z9, V8))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))))), implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z9, V8))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z9, V8))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(V8, implies(Z9, V8))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8)))))), true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.10 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9)))), implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true, ifeq(is_a_theorem(implies(implies(implies(W9, V9), implies(U9, T9)), implies(S9, implies(implies(T9, W9), implies(U9, W9))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))), implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.10 = { by axiom 2 (condensed_detachment) }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z9)), implies(implies(W8, V8), implies(implies(Z9, V8), implies(W8, V8)))), implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))))), true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z9)), implies(implies(W8, V8), implies(implies(Z9, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z9)), implies(implies(W8, V8), implies(implies(Z9, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V8, implies(W8, V8)), implies(W8, Z9)), implies(implies(W8, V8), implies(implies(Z9, V8), implies(W8, V8))))), true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.31/7.11 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.11 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.12 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10)))), implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8)))))), true, ifeq(is_a_theorem(implies(implies(implies(X10, Y10), implies(Z10, W10)), implies(V10, implies(implies(W10, X10), implies(Z10, X10))))), true, is_a_theorem(implies(implies(implies(implies(Z9, V8), implies(W8, V8)), implies(V8, implies(W8, V8))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 2 (condensed_detachment) }
% 42.31/7.12 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.12 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8)))), implies(implies(W8, V8), implies(V8, implies(W8, V8))))), true, ifeq(is_a_theorem(implies(implies(implies(U8, T8), implies(S8, X9)), implies(Y9, implies(implies(X9, U8), implies(S8, U8))))), true, is_a_theorem(implies(implies(W8, V8), implies(V8, implies(W8, V8)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 2 (condensed_detachment) }
% 42.31/7.12 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 1 (ifeq_axiom) }
% 42.31/7.12 ifeq(ifeq(is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.12 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.12 = { by axiom 2 (condensed_detachment) R->L }
% 42.31/7.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.13 = { by axiom 1 (ifeq_axiom) R->L }
% 42.31/7.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.31/7.13 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.31/7.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.13 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.13 = { by axiom 2 (condensed_detachment) R->L }
% 42.83/7.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(T10, implies(V11, T10))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))))), implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(T10, implies(V11, T10))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10)))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.14 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.83/7.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(T10, implies(V11, T10))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10)))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.14 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(T10, implies(V11, T10))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10)))))), true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.14 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.83/7.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.14 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11)))), implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true, ifeq(is_a_theorem(implies(implies(implies(U11, T11), implies(S11, X12)), implies(Y12, implies(implies(X12, U11), implies(S11, U11))))), true, is_a_theorem(implies(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))), implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.15 = { by axiom 2 (condensed_detachment) }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.15 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.15 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.15 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.15 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 2 (condensed_detachment) R->L }
% 42.83/7.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T10, implies(U10, T10)), implies(U10, V11)), implies(implies(U10, T10), implies(implies(V11, T10), implies(U10, T10)))), implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))))), true, ifeq(is_a_theorem(implies(implies(implies(T10, implies(U10, T10)), implies(U10, V11)), implies(implies(U10, T10), implies(implies(V11, T10), implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.83/7.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T10, implies(U10, T10)), implies(U10, V11)), implies(implies(U10, T10), implies(implies(V11, T10), implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T10, implies(U10, T10)), implies(U10, V11)), implies(implies(U10, T10), implies(implies(V11, T10), implies(U10, T10))))), true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.83/7.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.16 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12)))), implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10)))))), true, ifeq(is_a_theorem(implies(implies(implies(Z12, W12), implies(V12, U12)), implies(T12, implies(implies(U12, Z12), implies(V12, Z12))))), true, is_a_theorem(implies(implies(implies(implies(V11, T10), implies(U10, T10)), implies(T10, implies(U10, T10))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true), true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.16 = { by axiom 2 (condensed_detachment) }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10)))), implies(implies(U10, T10), implies(T10, implies(U10, T10))))), true, ifeq(is_a_theorem(implies(implies(implies(S10, X11), implies(Y11, Z11)), implies(W11, implies(implies(Z11, S10), implies(Y11, S10))))), true, is_a_theorem(implies(implies(U10, T10), implies(T10, implies(U10, T10)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 2 (condensed_detachment) }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 1 (ifeq_axiom) }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 2 (condensed_detachment) R->L }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.17 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.83/7.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.18 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.18 = { by axiom 2 (condensed_detachment) R->L }
% 42.83/7.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.18 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.18 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 42.83/7.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.19 = { by axiom 1 (ifeq_axiom) R->L }
% 42.83/7.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.19 = { by axiom 2 (condensed_detachment) R->L }
% 42.83/7.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(X13, implies(T13, X13))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))))), implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(X13, implies(T13, X13))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13)))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.19 = { by axiom 3 (ic_JLukasiewicz_4) }
% 42.83/7.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(X13, implies(T13, X13))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13)))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 42.83/7.20 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(X13, implies(T13, X13))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13)))))), true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.20 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.19/7.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.20 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13)))), implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true, ifeq(is_a_theorem(implies(implies(implies(S13, X14), implies(Y14, Z14)), implies(W14, implies(implies(Z14, S13), implies(Y14, S13))))), true, is_a_theorem(implies(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))), implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.21 = { by axiom 2 (condensed_detachment) }
% 43.19/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.21 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.21 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.21 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.19/7.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.22 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.22 = { by axiom 2 (condensed_detachment) R->L }
% 43.19/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X13, implies(S12, X13)), implies(S12, T13)), implies(implies(S12, X13), implies(implies(T13, X13), implies(S12, X13)))), implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))))), true, ifeq(is_a_theorem(implies(implies(implies(X13, implies(S12, X13)), implies(S12, T13)), implies(implies(S12, X13), implies(implies(T13, X13), implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.22 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.19/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X13, implies(S12, X13)), implies(S12, T13)), implies(implies(S12, X13), implies(implies(T13, X13), implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.22 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X13, implies(S12, X13)), implies(S12, T13)), implies(implies(S12, X13), implies(implies(T13, X13), implies(S12, X13))))), true, is_a_theorem(implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.19/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14)))), implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13)))))), true, ifeq(is_a_theorem(implies(implies(implies(V14, U14), implies(T14, S14)), implies(X15, implies(implies(S14, V14), implies(T14, V14))))), true, is_a_theorem(implies(implies(implies(implies(T13, X13), implies(S12, X13)), implies(X13, implies(S12, X13))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 2 (condensed_detachment) }
% 43.19/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13)))), implies(implies(S12, X13), implies(X13, implies(S12, X13))))), true, ifeq(is_a_theorem(implies(implies(implies(Y13, Z13), implies(W13, V13)), implies(U13, implies(implies(V13, Y13), implies(W13, Y13))))), true, is_a_theorem(implies(implies(S12, X13), implies(X13, implies(S12, X13)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 2 (condensed_detachment) }
% 43.19/7.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.23 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.24 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.24 = { by axiom 2 (condensed_detachment) R->L }
% 43.19/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.24 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.24 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.19/7.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.25 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.25 = { by axiom 2 (condensed_detachment) R->L }
% 43.19/7.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.25 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.26 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.19/7.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.26 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.26 = { by axiom 2 (condensed_detachment) R->L }
% 43.19/7.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(Z15, implies(X16, Z15))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))))), implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(Z15, implies(X16, Z15))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15)))))), true, is_a_theorem(implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.27 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.19/7.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(Z15, implies(X16, Z15))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15)))))), true, is_a_theorem(implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.27 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(Z15, implies(X16, Z15))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15)))))), true, is_a_theorem(implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.28 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.19/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.28 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16)))), implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y16, Z16), implies(W16, V16)), implies(U16, implies(implies(V16, Y16), implies(W16, Y16))))), true, is_a_theorem(implies(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.28 = { by axiom 2 (condensed_detachment) }
% 43.19/7.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.29 = { by axiom 1 (ifeq_axiom) }
% 43.19/7.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.29 = { by axiom 1 (ifeq_axiom) R->L }
% 43.19/7.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.19/7.29 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.19/7.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.31 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.31 = { by axiom 2 (condensed_detachment) R->L }
% 43.70/7.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z15, implies(Y15, Z15)), implies(Y15, X16)), implies(implies(Y15, Z15), implies(implies(X16, Z15), implies(Y15, Z15)))), implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z15, implies(Y15, Z15)), implies(Y15, X16)), implies(implies(Y15, Z15), implies(implies(X16, Z15), implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.31 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.70/7.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z15, implies(Y15, Z15)), implies(Y15, X16)), implies(implies(Y15, Z15), implies(implies(X16, Z15), implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.32 = { by axiom 1 (ifeq_axiom) }
% 43.70/7.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z15, implies(Y15, Z15)), implies(Y15, X16)), implies(implies(Y15, Z15), implies(implies(X16, Z15), implies(Y15, Z15))))), true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.32 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.70/7.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.32 = { by axiom 1 (ifeq_axiom) }
% 43.70/7.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16)))), implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))))), true, ifeq(is_a_theorem(implies(implies(implies(T16, S16), implies(X17, Y17)), implies(Z17, implies(implies(Y17, T16), implies(X17, T16))))), true, is_a_theorem(implies(implies(implies(implies(X16, Z15), implies(Y15, Z15)), implies(Z15, implies(Y15, Z15))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.32 = { by axiom 2 (condensed_detachment) }
% 43.70/7.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.33 = { by axiom 1 (ifeq_axiom) }
% 43.70/7.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15)))), implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))))), true, ifeq(is_a_theorem(implies(implies(implies(W15, V15), implies(U15, T15)), implies(S15, implies(implies(T15, W15), implies(U15, W15))))), true, is_a_theorem(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.33 = { by axiom 2 (condensed_detachment) }
% 43.70/7.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.33 = { by axiom 1 (ifeq_axiom) }
% 43.70/7.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.34 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.34 = { by axiom 2 (condensed_detachment) R->L }
% 43.70/7.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.34 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.35 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.70/7.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.35 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.36 = { by axiom 2 (condensed_detachment) R->L }
% 43.70/7.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.36 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.37 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 43.70/7.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.38 = { by axiom 1 (ifeq_axiom) R->L }
% 43.70/7.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.38 = { by axiom 2 (condensed_detachment) R->L }
% 43.70/7.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(V17, implies(Z18, V17))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))))), implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(V17, implies(Z18, V17))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17)))))), true, is_a_theorem(implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.39 = { by axiom 3 (ic_JLukasiewicz_4) }
% 43.70/7.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(V17, implies(Z18, V17))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17)))))), true, is_a_theorem(implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 43.70/7.40 = { by axiom 1 (ifeq_axiom) }
% 43.70/7.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(V17, implies(Z18, V17))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17)))))), true, is_a_theorem(implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.40 = { by axiom 3 (ic_JLukasiewicz_4) }
% 44.21/7.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.41 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18)))), implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true, ifeq(is_a_theorem(implies(implies(implies(W18, V18), implies(U18, T18)), implies(S18, implies(implies(T18, W18), implies(U18, W18))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))), implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.41 = { by axiom 2 (condensed_detachment) }
% 44.21/7.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.42 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.42 = { by axiom 1 (ifeq_axiom) R->L }
% 44.21/7.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.43 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 44.21/7.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.43 = { by axiom 1 (ifeq_axiom) R->L }
% 44.21/7.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.44 = { by axiom 2 (condensed_detachment) R->L }
% 44.21/7.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V17, implies(W17, V17)), implies(W17, Z18)), implies(implies(W17, V17), implies(implies(Z18, V17), implies(W17, V17)))), implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))))), true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, V17)), implies(W17, Z18)), implies(implies(W17, V17), implies(implies(Z18, V17), implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.44 = { by axiom 3 (ic_JLukasiewicz_4) }
% 44.21/7.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, V17)), implies(W17, Z18)), implies(implies(W17, V17), implies(implies(Z18, V17), implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.45 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V17, implies(W17, V17)), implies(W17, Z18)), implies(implies(W17, V17), implies(implies(Z18, V17), implies(W17, V17))))), true, is_a_theorem(implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.45 = { by axiom 3 (ic_JLukasiewicz_4) }
% 44.21/7.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.46 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19)))), implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17)))))), true, ifeq(is_a_theorem(implies(implies(implies(X19, Y19), implies(Z19, W19)), implies(V19, implies(implies(W19, X19), implies(Z19, X19))))), true, is_a_theorem(implies(implies(implies(implies(Z18, V17), implies(W17, V17)), implies(V17, implies(W17, V17))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.46 = { by axiom 2 (condensed_detachment) }
% 44.21/7.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.47 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17)))), implies(implies(W17, V17), implies(V17, implies(W17, V17))))), true, ifeq(is_a_theorem(implies(implies(implies(U17, T17), implies(S17, X18)), implies(Y18, implies(implies(X18, U17), implies(S17, U17))))), true, is_a_theorem(implies(implies(W17, V17), implies(V17, implies(W17, V17)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.47 = { by axiom 2 (condensed_detachment) }
% 44.21/7.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.48 = { by axiom 1 (ifeq_axiom) }
% 44.21/7.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.48 = { by axiom 1 (ifeq_axiom) R->L }
% 44.21/7.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.49 = { by axiom 2 (condensed_detachment) R->L }
% 44.21/7.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.21/7.49 = { by axiom 1 (ifeq_axiom) R->L }
% 44.21/7.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.50 = { by axiom 2 (condensed_detachment) R->L }
% 44.72/7.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z20, W20), implies(V20, U20)), implies(T20, implies(implies(U20, Z20), implies(V20, Z20)))), implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z20, W20), implies(V20, U20)), implies(T20, implies(implies(U20, Z20), implies(V20, Z20))))), true, is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, 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b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.51 = { by axiom 1 (ifeq_axiom) R->L }
% 44.72/7.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z20, W20), implies(V20, U20)), implies(T20, implies(implies(U20, Z20), implies(V20, Z20)))), implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), 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% 44.72/7.53 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 44.72/7.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), S20)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, 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c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, 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% 44.72/7.53 = { by axiom 1 (ifeq_axiom) R->L }
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implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, 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% 44.72/7.54 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 44.72/7.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), S20)), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), 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% 44.72/7.56 = { by axiom 2 (condensed_detachment) }
% 44.72/7.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z20, W20), implies(V20, U20)), implies(T20, implies(implies(U20, Z20), implies(V20, Z20))))), true, is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.56 = { by axiom 1 (ifeq_axiom) }
% 44.72/7.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z20, W20), implies(V20, U20)), implies(T20, implies(implies(U20, Z20), implies(V20, Z20))))), true, is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.57 = { by axiom 3 (ic_JLukasiewicz_4) }
% 44.72/7.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.58 = { by axiom 1 (ifeq_axiom) }
% 44.72/7.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 44.72/7.59 = { by axiom 1 (ifeq_axiom) R->L }
% 44.72/7.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.61 = { by axiom 2 (condensed_detachment) R->L }
% 45.23/7.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), 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implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), 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implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.62 = { by axiom 1 (ifeq_axiom) R->L }
% 45.23/7.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21)))), implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), 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c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), 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is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.64 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 45.23/7.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(S20, implies(implies(a, b), 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implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), 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implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, 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% 45.23/7.65 = { by axiom 1 (ifeq_axiom) R->L }
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% 45.23/7.67 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.68 = { by axiom 2 (condensed_detachment) }
% 45.23/7.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.69 = { by axiom 1 (ifeq_axiom) }
% 45.23/7.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X21, Y21), implies(Z21, W21)), implies(V21, implies(implies(W21, X21), implies(Z21, X21))))), true, is_a_theorem(implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.23/7.70 = { by axiom 3 (ic_JLukasiewicz_4) }
% 45.72/7.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.70 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S20, implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19)))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.72 = { by axiom 2 (condensed_detachment) }
% 45.72/7.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.72 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U19, T19), implies(S19, X20)), implies(Y20, implies(implies(X20, U19), implies(S19, U19))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.73 = { by axiom 3 (ic_JLukasiewicz_4) }
% 45.72/7.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.73 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.73 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.74 = { by axiom 1 (ifeq_axiom) R->L }
% 45.72/7.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.74 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 45.72/7.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(W17, V17), implies(V17, implies(W17, V17))), implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.74 = { by axiom 2 (condensed_detachment) }
% 45.72/7.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.75 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.75 = { by axiom 1 (ifeq_axiom) R->L }
% 45.72/7.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.76 = { by axiom 2 (condensed_detachment) R->L }
% 45.72/7.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.76 = { by axiom 1 (ifeq_axiom) R->L }
% 45.72/7.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.77 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 45.72/7.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.77 = { by axiom 1 (ifeq_axiom) R->L }
% 45.72/7.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21)))), implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), 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is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, 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c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.78 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 45.72/7.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), 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implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.79 = { by axiom 2 (condensed_detachment) }
% 45.72/7.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.79 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U21, T21), implies(S21, X22)), implies(Y22, implies(implies(X22, U21), implies(S21, U21))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.79 = { by axiom 3 (ic_JLukasiewicz_4) }
% 45.72/7.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.79 = { by axiom 1 (ifeq_axiom) }
% 45.72/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Y15, Z15), implies(Z15, implies(Y15, Z15))), implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.80 = { by axiom 2 (condensed_detachment) }
% 45.72/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 45.72/7.80 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.80 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.80 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(S12, X13), implies(X13, implies(S12, X13))), implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.80 = { by axiom 2 (condensed_detachment) }
% 46.23/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.80 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.80 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.80 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.81 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b))), implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(b, c), implies(a, c))), implies(a, b)), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(a, b)))), true, is_a_theorem(implies(implies(implies(U10, T10), implies(T10, implies(U10, T10))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 2 (condensed_detachment) }
% 46.23/7.81 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.81 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.81 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.81 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.82 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.82 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.82 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.83 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.83 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.83 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.83 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(W22, implies(Y23, W22))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))))), implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(W22, implies(Y23, W22))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22)))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.84 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.23/7.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(W22, implies(Y23, W22))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22)))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.84 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.84 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(W22, implies(Y23, W22))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22)))))), true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.84 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.23/7.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.85 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23)))), implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z23, W23), implies(V23, U23)), implies(T23, implies(implies(U23, Z23), implies(V23, Z23))))), true, is_a_theorem(implies(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.85 = { by axiom 2 (condensed_detachment) }
% 46.23/7.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.85 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.85 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.86 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.86 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.86 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W22, implies(Z22, W22)), implies(Z22, Y23)), implies(implies(Z22, W22), implies(implies(Y23, W22), implies(Z22, W22)))), implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))))), true, ifeq(is_a_theorem(implies(implies(implies(W22, implies(Z22, W22)), implies(Z22, Y23)), implies(implies(Z22, W22), implies(implies(Y23, W22), implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.86 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.23/7.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W22, implies(Z22, W22)), implies(Z22, Y23)), implies(implies(Z22, W22), implies(implies(Y23, W22), implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.87 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W22, implies(Z22, W22)), implies(Z22, Y23)), implies(implies(Z22, W22), implies(implies(Y23, W22), implies(Z22, W22))))), true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.87 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.23/7.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.87 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.87 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23)))), implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))))), true, ifeq(is_a_theorem(implies(implies(implies(S23, X24), implies(Y24, Z24)), implies(W24, implies(implies(Z24, S23), implies(Y24, S23))))), true, is_a_theorem(implies(implies(implies(implies(Y23, W22), implies(Z22, W22)), implies(W22, implies(Z22, W22))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true), true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.87 = { by axiom 2 (condensed_detachment) }
% 46.23/7.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.88 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22)))), implies(implies(Z22, W22), implies(W22, implies(Z22, W22))))), true, ifeq(is_a_theorem(implies(implies(implies(V22, U22), implies(T22, S22)), implies(X23, implies(implies(S22, V22), implies(T22, V22))))), true, is_a_theorem(implies(implies(Z22, W22), implies(W22, implies(Z22, W22)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.88 = { by axiom 2 (condensed_detachment) }
% 46.23/7.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.88 = { by axiom 1 (ifeq_axiom) }
% 46.23/7.88 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.88 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.88 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.88 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.89 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.89 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.23/7.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.89 = { by axiom 1 (ifeq_axiom) R->L }
% 46.23/7.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.23/7.90 = { by axiom 2 (condensed_detachment) R->L }
% 46.23/7.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.90 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.91 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.74/7.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.91 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.91 = { by axiom 2 (condensed_detachment) R->L }
% 46.74/7.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(U24, implies(W25, U24))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))))), implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(U24, implies(W25, U24))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24)))))), true, is_a_theorem(implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.92 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.74/7.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(U24, implies(W25, U24))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24)))))), true, is_a_theorem(implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.92 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(U24, implies(W25, U24))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24)))))), true, is_a_theorem(implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.93 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.74/7.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.93 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25)))), implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true, ifeq(is_a_theorem(implies(implies(implies(V25, U25), implies(T25, S25)), implies(X26, implies(implies(S25, V25), implies(T25, V25))))), true, is_a_theorem(implies(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))), implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.93 = { by axiom 2 (condensed_detachment) }
% 46.74/7.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.94 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.94 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.94 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.74/7.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.95 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.95 = { by axiom 2 (condensed_detachment) R->L }
% 46.74/7.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U24, implies(V24, U24)), implies(V24, W25)), implies(implies(V24, U24), implies(implies(W25, U24), implies(V24, U24)))), implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))))), true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, U24)), implies(V24, W25)), implies(implies(V24, U24), implies(implies(W25, U24), implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.96 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.74/7.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, U24)), implies(V24, W25)), implies(implies(V24, U24), implies(implies(W25, U24), implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.96 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U24, implies(V24, U24)), implies(V24, W25)), implies(implies(V24, U24), implies(implies(W25, U24), implies(V24, U24))))), true, is_a_theorem(implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.96 = { by axiom 3 (ic_JLukasiewicz_4) }
% 46.74/7.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.97 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26)))), implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y26, Z26), implies(W26, V26)), implies(U26, implies(implies(V26, Y26), implies(W26, Y26))))), true, is_a_theorem(implies(implies(implies(implies(W25, U24), implies(V24, U24)), implies(U24, implies(V24, U24))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.97 = { by axiom 2 (condensed_detachment) }
% 46.74/7.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.97 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24)))), implies(implies(V24, U24), implies(U24, implies(V24, U24))))), true, ifeq(is_a_theorem(implies(implies(implies(T24, S24), implies(X25, Y25)), implies(Z25, implies(implies(Y25, T24), implies(X25, T24))))), true, is_a_theorem(implies(implies(V24, U24), implies(U24, implies(V24, U24)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.97 = { by axiom 2 (condensed_detachment) }
% 46.74/7.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.98 = { by axiom 1 (ifeq_axiom) }
% 46.74/7.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.98 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.98 = { by axiom 2 (condensed_detachment) R->L }
% 46.74/7.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.99 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/7.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/7.99 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.74/7.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.00 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/8.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.00 = { by axiom 2 (condensed_detachment) R->L }
% 46.74/8.00 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.01 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/8.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.01 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 46.74/8.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.02 = { by axiom 1 (ifeq_axiom) R->L }
% 46.74/8.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.02 = { by axiom 2 (condensed_detachment) R->L }
% 46.74/8.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(S26, implies(U27, S26))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))))), implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(S26, implies(U27, S26))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26)))))), true, is_a_theorem(implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 46.74/8.03 = { by axiom 3 (ic_JLukasiewicz_4) }
% 47.41/8.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(S26, implies(U27, S26))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26)))))), true, is_a_theorem(implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.04 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(S26, implies(U27, S26))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26)))))), true, is_a_theorem(implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.04 = { by axiom 3 (ic_JLukasiewicz_4) }
% 47.41/8.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.05 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27)))), implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true, ifeq(is_a_theorem(implies(implies(implies(T27, S27), implies(X28, Y28)), implies(Z28, implies(implies(Y28, T27), implies(X28, T27))))), true, is_a_theorem(implies(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))), implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.05 = { by axiom 2 (condensed_detachment) }
% 47.41/8.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.06 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.06 = { by axiom 1 (ifeq_axiom) R->L }
% 47.41/8.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.07 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 47.41/8.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.07 = { by axiom 1 (ifeq_axiom) R->L }
% 47.41/8.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.08 = { by axiom 2 (condensed_detachment) R->L }
% 47.41/8.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S26, implies(T26, S26)), implies(T26, U27)), implies(implies(T26, S26), implies(implies(U27, S26), implies(T26, S26)))), implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))))), true, ifeq(is_a_theorem(implies(implies(implies(S26, implies(T26, S26)), implies(T26, U27)), implies(implies(T26, S26), implies(implies(U27, S26), implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.09 = { by axiom 3 (ic_JLukasiewicz_4) }
% 47.41/8.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S26, implies(T26, S26)), implies(T26, U27)), implies(implies(T26, S26), implies(implies(U27, S26), implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.09 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S26, implies(T26, S26)), implies(T26, U27)), implies(implies(T26, S26), implies(implies(U27, S26), implies(T26, S26))))), true, is_a_theorem(implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.10 = { by axiom 3 (ic_JLukasiewicz_4) }
% 47.41/8.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.10 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28)))), implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26)))))), true, ifeq(is_a_theorem(implies(implies(implies(W28, V28), implies(U28, T28)), implies(S28, implies(implies(T28, W28), implies(U28, W28))))), true, is_a_theorem(implies(implies(implies(implies(U27, S26), implies(T26, S26)), implies(S26, implies(T26, S26))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true), true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.11 = { by axiom 2 (condensed_detachment) }
% 47.41/8.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.11 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27)))), implies(implies(T26, S26), implies(S26, implies(T26, S26))))), true, ifeq(is_a_theorem(implies(implies(implies(X27, Y27), implies(Z27, W27)), implies(V27, implies(implies(W27, X27), implies(Z27, X27))))), true, is_a_theorem(implies(implies(T26, S26), implies(S26, implies(T26, S26)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.11 = { by axiom 2 (condensed_detachment) }
% 47.41/8.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.12 = { by axiom 1 (ifeq_axiom) }
% 47.41/8.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.41/8.13 = { by axiom 1 (ifeq_axiom) R->L }
% 47.41/8.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.13 = { by axiom 2 (condensed_detachment) R->L }
% 47.94/8.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.14 = { by axiom 1 (ifeq_axiom) R->L }
% 47.94/8.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), 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implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.15 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 47.94/8.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.15 = { by axiom 1 (ifeq_axiom) R->L }
% 47.94/8.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.16 = { by axiom 2 (condensed_detachment) R->L }
% 47.94/8.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.17 = { by axiom 1 (ifeq_axiom) R->L }
% 47.94/8.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.18 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 47.94/8.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.19 = { by axiom 1 (ifeq_axiom) R->L }
% 47.94/8.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 47.94/8.20 = { by axiom 2 (condensed_detachment) R->L }
% 48.28/8.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(Y29, implies(S29, Y29))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))))), implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(Y29, implies(S29, Y29))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29)))))), true, is_a_theorem(implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.21 = { by axiom 3 (ic_JLukasiewicz_4) }
% 48.28/8.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(Y29, implies(S29, Y29))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29)))))), true, is_a_theorem(implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.22 = { by axiom 1 (ifeq_axiom) }
% 48.28/8.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(Y29, implies(S29, Y29))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29)))))), true, is_a_theorem(implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.23 = { by axiom 3 (ic_JLukasiewicz_4) }
% 48.28/8.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.23 = { by axiom 1 (ifeq_axiom) }
% 48.28/8.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30)))), implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true, ifeq(is_a_theorem(implies(implies(implies(X30, Y30), implies(Z30, W30)), implies(V30, implies(implies(W30, X30), implies(Z30, X30))))), true, is_a_theorem(implies(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.24 = { by axiom 2 (condensed_detachment) }
% 48.28/8.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.25 = { by axiom 1 (ifeq_axiom) }
% 48.28/8.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.26 = { by axiom 1 (ifeq_axiom) R->L }
% 48.28/8.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.27 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 48.28/8.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.27 = { by axiom 1 (ifeq_axiom) R->L }
% 48.28/8.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.28 = { by axiom 2 (condensed_detachment) R->L }
% 48.28/8.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y29, implies(X29, Y29)), implies(X29, S29)), implies(implies(X29, Y29), implies(implies(S29, Y29), implies(X29, Y29)))), implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))))), true, ifeq(is_a_theorem(implies(implies(implies(Y29, implies(X29, Y29)), implies(X29, S29)), implies(implies(X29, Y29), implies(implies(S29, Y29), implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.28/8.29 = { by axiom 3 (ic_JLukasiewicz_4) }
% 48.28/8.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y29, implies(X29, Y29)), implies(X29, S29)), implies(implies(X29, Y29), implies(implies(S29, Y29), implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.30 = { by axiom 1 (ifeq_axiom) }
% 48.79/8.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y29, implies(X29, Y29)), implies(X29, S29)), implies(implies(X29, Y29), implies(implies(S29, Y29), implies(X29, Y29))))), true, is_a_theorem(implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.31 = { by axiom 3 (ic_JLukasiewicz_4) }
% 48.79/8.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.32 = { by axiom 1 (ifeq_axiom) }
% 48.79/8.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30)))), implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))))), true, ifeq(is_a_theorem(implies(implies(implies(U30, T30), implies(S30, X31)), implies(Y31, implies(implies(X31, U30), implies(S30, U30))))), true, is_a_theorem(implies(implies(implies(implies(S29, Y29), implies(X29, Y29)), implies(Y29, implies(X29, Y29))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), 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implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.32 = { by axiom 2 (condensed_detachment) }
% 48.79/8.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.33 = { by axiom 1 (ifeq_axiom) }
% 48.79/8.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29)))), implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))))), true, ifeq(is_a_theorem(implies(implies(implies(Z29, W29), implies(V29, U29)), implies(T29, implies(implies(U29, Z29), implies(V29, Z29))))), true, is_a_theorem(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.33 = { by axiom 2 (condensed_detachment) }
% 48.79/8.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.34 = { by axiom 1 (ifeq_axiom) }
% 48.79/8.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.35 = { by axiom 1 (ifeq_axiom) R->L }
% 48.79/8.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.36 = { by axiom 2 (condensed_detachment) R->L }
% 48.79/8.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31)))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31))))), true, is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 48.79/8.38 = { by axiom 1 (ifeq_axiom) R->L }
% 48.79/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31)))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), 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implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, 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% 48.79/8.39 = { by axiom 2 (condensed_detachment) R->L }
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is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 49.30/8.42 = { by axiom 1 (ifeq_axiom) R->L }
% 49.30/8.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(S31, X32), implies(Y32, Z32)), implies(W32, implies(implies(Z32, S31), implies(Y32, S31)))), implies(implies(implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(S31, X32), implies(Y32, Z32)), implies(W32, implies(implies(Z32, S31), implies(Y32, S31))))), true, is_a_theorem(implies(implies(implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31)))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31))))), true, is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 49.30/8.45 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 49.30/8.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), V32)), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, is_a_theorem(implies(implies(implies(implies(S31, X32), implies(Y32, Z32)), implies(W32, 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% 49.30/8.46 = { by axiom 1 (ifeq_axiom) R->L }
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% 49.30/8.48 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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% 49.30/8.50 = { by axiom 2 (condensed_detachment) }
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b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 49.80/8.51 = { by axiom 1 (ifeq_axiom) }
% 49.80/8.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S31, X32), implies(Y32, Z32)), implies(W32, implies(implies(Z32, S31), implies(Y32, S31))))), true, is_a_theorem(implies(implies(implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31)))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), 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c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, 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% 49.80/8.52 = { by axiom 3 (ic_JLukasiewicz_4) }
% 49.80/8.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), 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implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), 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% 49.80/8.54 = { by axiom 1 (ifeq_axiom) }
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% 49.80/8.57 = { by axiom 1 (ifeq_axiom) R->L }
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% 49.80/8.59 = { by axiom 2 (condensed_detachment) R->L }
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% 50.31/8.62 = { by axiom 1 (ifeq_axiom) R->L }
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% 50.31/8.67 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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% 50.81/8.70 = { by axiom 1 (ifeq_axiom) R->L }
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% 50.81/8.72 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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implies(a, c)))), true), true)
% 50.81/8.75 = { by axiom 2 (condensed_detachment) }
% 50.81/8.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(U32, T32), implies(S32, X33)), implies(Y33, implies(implies(X33, U32), implies(S32, U32))))), true, is_a_theorem(implies(implies(implies(implies(implies(V32, implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), 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implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), 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implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), 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% 50.81/8.77 = { by axiom 1 (ifeq_axiom) }
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% 50.81/8.78 = { by axiom 3 (ic_JLukasiewicz_4) }
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% 50.81/8.79 = { by axiom 1 (ifeq_axiom) }
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implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.80 = { by axiom 2 (condensed_detachment) }
% 51.31/8.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31))))), true, is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.81 = { by axiom 1 (ifeq_axiom) }
% 51.31/8.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z31, W31), implies(V31, U31)), implies(T31, implies(implies(U31, Z31), implies(V31, Z31))))), true, is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.82 = { by axiom 3 (ic_JLukasiewicz_4) }
% 51.31/8.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.83 = { by axiom 1 (ifeq_axiom) }
% 51.31/8.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, 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implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), 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% 51.31/8.84 = { by axiom 1 (ifeq_axiom) R->L }
% 51.31/8.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.84 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 51.31/8.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(X29, Y29), implies(Y29, implies(X29, Y29))), implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.85 = { by axiom 2 (condensed_detachment) }
% 51.31/8.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.86 = { by axiom 1 (ifeq_axiom) }
% 51.31/8.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.86 = { by axiom 1 (ifeq_axiom) R->L }
% 51.31/8.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.87 = { by axiom 2 (condensed_detachment) R->L }
% 51.31/8.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33)))), implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.88 = { by axiom 1 (ifeq_axiom) R->L }
% 51.31/8.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33)))), implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), 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S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.31/8.89 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 51.84/8.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, is_a_theorem(implies(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33)))), implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), 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b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), 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% 51.84/8.90 = { by axiom 1 (ifeq_axiom) R->L }
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% 51.84/8.91 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
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implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.92 = { by axiom 2 (condensed_detachment) }
% 51.84/8.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.93 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z33, W33), implies(V33, U33)), implies(T33, implies(implies(U33, Z33), implies(V33, Z33))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.93 = { by axiom 3 (ic_JLukasiewicz_4) }
% 51.84/8.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.94 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true, is_a_theorem(implies(implies(implies(T26, S26), implies(S26, implies(T26, S26))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.94 = { by axiom 2 (condensed_detachment) }
% 51.84/8.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.94 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.95 = { by axiom 1 (ifeq_axiom) R->L }
% 51.84/8.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.95 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 51.84/8.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(V24, U24), implies(U24, implies(V24, U24))), implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.95 = { by axiom 2 (condensed_detachment) }
% 51.84/8.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.95 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.96 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 1 (ifeq_axiom) R->L }
% 51.84/8.96 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 3 (ic_JLukasiewicz_4) R->L }
% 51.84/8.96 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, is_a_theorem(implies(implies(implies(Z22, W22), implies(W22, implies(Z22, W22))), implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 2 (condensed_detachment) }
% 51.84/8.96 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.96 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true, is_a_theorem(implies(implies(implies(W8, V8), implies(V8, implies(W8, V8))), implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c)))))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 2 (condensed_detachment) }
% 51.84/8.96 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 1 (ifeq_axiom) }
% 51.84/8.96 ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c)))), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(a, b), implies(implies(b, c), implies(a, c))))), true, is_a_theorem(implies(implies(a, b), implies(implies(b, c), implies(a, c)))), true), true)
% 51.84/8.96 = { by axiom 2 (condensed_detachment) }
% 51.84/8.96 true
% 51.84/8.96 % SZS output end Proof
% 51.84/8.96
% 51.84/8.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------