%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 11:48:59 AM UTC 2026
% Result : Unsatisfiable 1.01s 0.61s
% Output : Proof 2.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 15:21:14 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.01/0.61 Command-line arguments: --flatten --complete-subsets
% 1.01/0.61
% 1.01/0.61 % SZS status Unsatisfiable
% 1.01/0.61
% 2.47/0.84 % SZS output start Proof
% 2.47/0.84 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.47/0.84 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.
% 2.47/0.85 Axiom 3 (ic_JLukasiewicz): is_a_theorem(implies(implies(implies(X, Y), Z), implies(implies(Z, X), implies(W, X)))) = true.
% 2.47/0.85
% 2.47/0.85 Goal 1 (prove_ic_2): is_a_theorem(implies(a, implies(b, a))) = true.
% 2.47/0.85 Proof:
% 2.47/0.85 is_a_theorem(implies(a, implies(b, a)))
% 2.47/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.86 ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true)
% 2.47/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.86 ifeq(true, true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 2 (condensed_detachment) R->L }
% 2.47/0.86 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.86 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 2 (condensed_detachment) R->L }
% 2.47/0.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W)))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 3 (ic_JLukasiewicz) }
% 2.47/0.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 1 (ifeq_axiom) }
% 2.47/0.86 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.86 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.87 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.87 = { by axiom 2 (condensed_detachment) R->L }
% 2.47/0.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a)))), implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.87 = { by axiom 3 (ic_JLukasiewicz) }
% 2.47/0.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.88 = { by axiom 1 (ifeq_axiom) }
% 2.47/0.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.88 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.89 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.47/0.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.89 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.89 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.47/0.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(a, implies(b, a))), implies(implies(a, S), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.89 = { by axiom 2 (condensed_detachment) }
% 2.47/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.90 = { by axiom 1 (ifeq_axiom) }
% 2.47/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.47/0.90 = { by axiom 1 (ifeq_axiom) R->L }
% 2.47/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.90 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))), implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, S), implies(a, implies(b, a))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(W, V), U), implies(implies(U, W), implies(T, W))), implies(implies(implies(a, implies(b, a)), a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 2 (condensed_detachment) }
% 2.27/0.90 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.90 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.90 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.90 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), a), implies(b, a)), implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), a), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 2 (condensed_detachment) }
% 2.27/0.90 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.90 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.90 ifeq(ifeq(is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 2 (condensed_detachment) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(X2, a)), implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(X2, a)), implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.91 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.91 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(X2, a)), implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a)))), implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(a, implies(b, a))), implies(X2, a)), implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))), implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 2 (condensed_detachment) }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), X2), implies(implies(X2, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), X2), implies(implies(X2, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(b, a)), X2), implies(implies(X2, a), implies(b, a))), implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(b, a)), X2), implies(implies(X2, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(X2, a), implies(b, a)), implies(a, implies(b, a))), implies(implies(b, a), implies(a, implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 2 (condensed_detachment) }
% 2.27/0.92 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.92 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2))), implies(implies(b, a), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, Z2), W2), implies(implies(W2, Y2), implies(V2, Y2)))), true, is_a_theorem(implies(implies(b, a), implies(a, implies(b, a)))), true), true), true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 2 (condensed_detachment) }
% 2.27/0.92 ifeq(ifeq(true, true, is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.92 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.92 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 2 (condensed_detachment) R->L }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 2 (condensed_detachment) R->L }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, ifeq(is_a_theorem(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2)))), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 3 (ic_JLukasiewicz) }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.93 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.93 = { by axiom 2 (condensed_detachment) R->L }
% 2.27/0.94 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.94 = { by axiom 3 (ic_JLukasiewicz) }
% 2.27/0.94 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.94 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.94 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.94 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.94 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.95 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.95 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.95 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.95 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.95 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.95 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Y, Y3), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.95 = { by axiom 2 (condensed_detachment) }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, Y3), implies(Y, implies(Z, Y))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(U2, T2), S2), implies(implies(S2, U2), implies(X3, U2))), implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)))), true), true), true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 2 (condensed_detachment) }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y)), implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Y), implies(Z, Y))), true, is_a_theorem(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(X, implies(Y, implies(Z, Y))))), true), true), true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.96 = { by axiom 2 (condensed_detachment) }
% 2.27/0.96 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 2 (condensed_detachment) R->L }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(Z3, Y)), implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.97 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.97 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(Z3, Y)), implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(Z3, Y)), implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z, Y), implies(Y, implies(Z, Y))), implies(Z3, Y)), implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))), implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 2 (condensed_detachment) }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Z3), implies(implies(Z3, Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.98 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Z3), implies(implies(Z3, Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.98 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, implies(Z, Y)), Z3), implies(implies(Z3, Y), implies(Z, Y))), implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y)))))), true, ifeq(is_a_theorem(implies(implies(implies(Y, implies(Z, Y)), Z3), implies(implies(Z3, Y), implies(Z, Y)))), true, is_a_theorem(implies(implies(implies(implies(Z3, Y), implies(Z, Y)), implies(Y, implies(Z, Y))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true), true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 2 (condensed_detachment) }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 1 (ifeq_axiom) R->L }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, ifeq(true, true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 3 (ic_JLukasiewicz) R->L }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3))), implies(implies(Z, Y), implies(Y, implies(Z, Y))))), true, ifeq(is_a_theorem(implies(implies(implies(W3, V3), U3), implies(implies(U3, W3), implies(T3, W3)))), true, is_a_theorem(implies(implies(Z, Y), implies(Y, implies(Z, Y)))), true), true), true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 2 (condensed_detachment) }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 1 (ifeq_axiom) }
% 2.27/0.99 ifeq(is_a_theorem(implies(implies(X, implies(Y, implies(Z, Y))), implies(a, implies(b, a)))), true, ifeq(is_a_theorem(implies(X, implies(Y, implies(Z, Y)))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 2.27/0.99 = { by axiom 2 (condensed_detachment) }
% 2.27/0.99 true
% 2.27/0.99 % SZS output end Proof
% 2.27/0.99
% 2.27/0.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------