%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 11:48:54 AM UTC 2026
% Result : Unsatisfiable 17.72s 2.74s
% Output : Proof 20.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL047-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 15:18:46 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.72/2.74 Command-line arguments: --flatten-regeneralise
% 17.72/2.74
% 17.72/2.74 % SZS status Unsatisfiable
% 17.72/2.74
% 19.32/3.02 % SZS output start Proof
% 19.32/3.02 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 19.32/3.02 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 19.32/3.02 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 19.32/3.02 Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 19.32/3.03 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 19.32/3.03
% 19.32/3.03 Goal 1 (prove_cn_18): is_a_theorem(implies(a, implies(b, a))) = true.
% 19.32/3.03 Proof:
% 19.32/3.03 is_a_theorem(implies(a, implies(b, a)))
% 19.32/3.03 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.03 ifeq(true, true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.03 = { by axiom 4 (condensed_detachment) R->L }
% 19.32/3.03 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(b, a), implies(b, a))), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.03 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.03 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.03 = { by axiom 4 (condensed_detachment) R->L }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(b, a), implies(not(implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 5 (cn_1) }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, a), implies(not(implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, a), implies(not(implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 2 (cn_3) }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.04 = { by axiom 3 (cn_2) R->L }
% 19.32/3.04 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(b, a), implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(implies(b, a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 4 (condensed_detachment) }
% 19.32/3.05 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.05 ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 4 (condensed_detachment) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 5 (cn_1) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 5 (cn_1) R->L }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a)))), implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 4 (condensed_detachment) }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.05 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.05 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 4 (condensed_detachment) R->L }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))), implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 5 (cn_1) }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 3 (cn_2) R->L }
% 19.32/3.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.06 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.07 = { by axiom 5 (cn_1) R->L }
% 19.32/3.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.07 = { by axiom 4 (condensed_detachment) }
% 19.32/3.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.07 = { by axiom 1 (ifeq_axiom) }
% 19.32/3.07 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.07 = { by axiom 1 (ifeq_axiom) R->L }
% 19.32/3.07 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 19.32/3.07 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.08 = { by axiom 5 (cn_1) }
% 20.67/3.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.08 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.08 = { by axiom 5 (cn_1) }
% 20.67/3.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.09 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, a)), implies(b, a)), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(not(implies(b, a)), implies(b, a))), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 4 (condensed_detachment) }
% 20.67/3.09 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a))), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 3 (cn_2) }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.09 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.09 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 2 (cn_3) R->L }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(not(implies(b, a))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(not(implies(b, a))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 5 (cn_1) R->L }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(not(not(implies(b, a))), implies(a, a))), implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(not(implies(b, a))), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))), implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 4 (condensed_detachment) }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.10 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.10 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(not(implies(a, a)), not(not(implies(b, a)))))), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 2 (cn_3) }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(a, a)))), true, ifeq(is_a_theorem(implies(a, implies(not(a), a))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 5 (cn_1) }
% 20.67/3.11 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(not(a), a))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.11 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(not(a), a))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 2 (cn_3) }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 3 (cn_2) R->L }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(a, a))), true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 4 (condensed_detachment) }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.12 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.12 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 5 (cn_1) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(a, a)), not(not(implies(b, a)))), implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(not(implies(a, a)), not(not(implies(b, a))))), true, is_a_theorem(implies(implies(not(not(implies(b, a))), implies(a, a)), implies(not(implies(a, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 4 (condensed_detachment) }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 5 (cn_1) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a))), implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(not(implies(b, a)), implies(not(implies(a, a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(not(implies(a, a)), implies(a, a)), implies(a, a)), implies(not(implies(b, a)), implies(a, a)))), true), true), true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 4 (condensed_detachment) }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.13 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, a)), implies(a, a)), implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a))))), true, ifeq(is_a_theorem(implies(not(implies(b, a)), implies(a, a))), true, is_a_theorem(implies(implies(implies(b, a), implies(b, a)), implies(implies(implies(a, a), implies(b, a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 4 (condensed_detachment) }
% 20.67/3.13 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.13 ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.13 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.13 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.13 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(a, a), implies(b, a))), implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a))))), true, ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.13 = { by axiom 5 (cn_1) }
% 20.67/3.13 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.13 ifeq(ifeq(is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.13 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.13 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 5 (cn_1) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 5 (cn_1) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(b, a))), implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))), implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 4 (condensed_detachment) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 5 (cn_1) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 3 (cn_2) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.14 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.14 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 5 (cn_1) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, a), implies(implies(not(a), a), a)), implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(b, a)), implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 4 (condensed_detachment) }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.15 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, implies(not(a), a))), implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a)))))), true, ifeq(is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 5 (cn_1) }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.15 = { by axiom 5 (cn_1) R->L }
% 20.67/3.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 5 (cn_1) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))), implies(implies(not(a), not(b)), implies(b, implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 4 (condensed_detachment) }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 2 (cn_3) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(not(b), a))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(not(b), a))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.16 = { by axiom 5 (cn_1) R->L }
% 20.67/3.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a))))), true, ifeq(is_a_theorem(implies(b, implies(not(b), a))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 4 (condensed_detachment) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) R->L }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 4 (condensed_detachment) R->L }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(not(a), not(b))), implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a)))))), true, ifeq(is_a_theorem(implies(a, implies(not(a), not(b)))), true, is_a_theorem(implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 5 (cn_1) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(not(a), not(b)))), true, is_a_theorem(implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(not(a), not(b)))), true, is_a_theorem(implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 2 (cn_3) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(b)), implies(b, implies(not(a), a))), implies(a, implies(b, implies(not(a), a))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(b, implies(not(a), a)))), true, is_a_theorem(implies(a, implies(b, implies(not(a), a)))), true), true), true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 4 (condensed_detachment) }
% 20.67/3.17 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.17 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a))), implies(a, implies(implies(a, a), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(b, implies(not(a), a)), implies(implies(a, a), implies(b, a)))), true, is_a_theorem(implies(a, implies(implies(a, a), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 4 (condensed_detachment) }
% 20.67/3.17 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 1 (ifeq_axiom) }
% 20.67/3.17 ifeq(is_a_theorem(implies(implies(implies(implies(a, a), implies(b, a)), implies(b, a)), implies(a, implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, a), implies(b, a)), implies(b, a))), true, is_a_theorem(implies(a, implies(b, a))), true), true)
% 20.67/3.17 = { by axiom 4 (condensed_detachment) }
% 20.67/3.17 true
% 20.67/3.17 % SZS output end Proof
% 20.67/3.17
% 20.67/3.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------