%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 115.54s 15.15s
% Output : Proof 151.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n011.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 27 15:19:00 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.54/15.15 Command-line arguments: --no-flatten-goal
% 115.54/15.15
% 115.54/15.15 % SZS status Unsatisfiable
% 115.54/15.15
% 141.78/18.50 % SZS output start Proof
% 141.78/18.50 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 141.78/18.50 Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 141.78/18.50 Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 141.78/18.50 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.
% 142.60/18.56 Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 142.60/18.56
% 142.60/18.56 Goal 1 (prove_cn_21): is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))) = true.
% 142.60/18.56 Proof:
% 142.60/18.56 is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c))))
% 142.60/18.56 = { by axiom 1 (ifeq_axiom) R->L }
% 142.60/18.56 ifeq(true, true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.56 = { by axiom 4 (condensed_detachment) R->L }
% 142.60/18.56 ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(b, c), c)), implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))))), true, ifeq(is_a_theorem(implies(b, implies(implies(b, c), c))), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.56 = { by axiom 5 (cn_1) }
% 142.60/18.56 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(implies(b, c), c))), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.57 = { by axiom 1 (ifeq_axiom) }
% 142.60/18.57 ifeq(ifeq(is_a_theorem(implies(b, implies(implies(b, c), c))), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.57 = { by axiom 1 (ifeq_axiom) R->L }
% 142.60/18.57 ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.57 = { by axiom 4 (condensed_detachment) R->L }
% 142.60/18.57 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.57 = { by axiom 1 (ifeq_axiom) R->L }
% 142.60/18.57 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.57 = { by axiom 4 (condensed_detachment) R->L }
% 142.60/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.58 = { by axiom 1 (ifeq_axiom) R->L }
% 142.60/18.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.58 = { by axiom 4 (condensed_detachment) R->L }
% 142.60/18.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.59 = { by axiom 2 (cn_3) }
% 142.60/18.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.59 = { by axiom 1 (ifeq_axiom) }
% 142.60/18.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 142.60/18.60 = { by axiom 5 (cn_1) }
% 143.34/18.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.60 = { by axiom 1 (ifeq_axiom) }
% 143.34/18.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.61 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.61 = { by axiom 3 (cn_2) R->L }
% 143.34/18.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.61 = { by axiom 4 (condensed_detachment) }
% 143.34/18.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.62 = { by axiom 1 (ifeq_axiom) }
% 143.34/18.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.62 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.62 = { by axiom 4 (condensed_detachment) R->L }
% 143.34/18.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.63 = { by axiom 5 (cn_1) }
% 143.34/18.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.63 = { by axiom 1 (ifeq_axiom) }
% 143.34/18.63 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.64 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.64 = { by axiom 4 (condensed_detachment) R->L }
% 143.34/18.64 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.65 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.65 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.65 = { by axiom 5 (cn_1) R->L }
% 143.34/18.66 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.66 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.67 = { by axiom 5 (cn_1) R->L }
% 143.34/18.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.67 = { by axiom 4 (condensed_detachment) }
% 143.34/18.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.68 = { by axiom 1 (ifeq_axiom) }
% 143.34/18.68 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.69 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.69 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.70 = { by axiom 4 (condensed_detachment) R->L }
% 143.34/18.70 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.70 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.71 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.71 = { by axiom 5 (cn_1) R->L }
% 143.34/18.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c)), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.72 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.72 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c)), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.74 = { by axiom 2 (cn_3) R->L }
% 143.34/18.74 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c)), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.74 = { by axiom 4 (condensed_detachment) }
% 143.34/18.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.75 = { by axiom 1 (ifeq_axiom) }
% 143.34/18.75 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.76 = { by axiom 1 (ifeq_axiom) R->L }
% 143.34/18.76 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 143.34/18.76 = { by axiom 5 (cn_1) R->L }
% 143.34/18.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true, is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.77 = { by axiom 1 (ifeq_axiom) R->L }
% 144.65/18.77 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.78 = { by axiom 3 (cn_2) R->L }
% 144.65/18.78 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), c), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.78 = { by axiom 4 (condensed_detachment) }
% 144.65/18.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.79 = { by axiom 1 (ifeq_axiom) }
% 144.65/18.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.79 = { by axiom 1 (ifeq_axiom) R->L }
% 144.65/18.79 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.80 = { by axiom 5 (cn_1) R->L }
% 144.65/18.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c)), implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))), c), implies(implies(b, c), c)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.80 = { by axiom 4 (condensed_detachment) }
% 144.65/18.80 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.81 = { by axiom 1 (ifeq_axiom) }
% 144.65/18.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.81 = { by axiom 1 (ifeq_axiom) R->L }
% 144.65/18.81 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.82 = { by axiom 4 (condensed_detachment) R->L }
% 144.65/18.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.82 = { by axiom 5 (cn_1) }
% 144.65/18.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.83 = { by axiom 1 (ifeq_axiom) }
% 144.65/18.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.84 = { by axiom 1 (ifeq_axiom) R->L }
% 144.65/18.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.85 = { by axiom 4 (condensed_detachment) R->L }
% 144.65/18.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.86 = { by axiom 5 (cn_1) }
% 144.65/18.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 144.65/18.87 = { by axiom 1 (ifeq_axiom) }
% 145.45/18.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.45/18.88 = { by axiom 1 (ifeq_axiom) R->L }
% 145.45/18.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.45/18.89 = { by axiom 5 (cn_1) R->L }
% 145.45/18.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.90 = { by axiom 1 (ifeq_axiom) R->L }
% 145.69/18.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.91 = { by axiom 4 (condensed_detachment) R->L }
% 145.69/18.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c)))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.93 = { by axiom 2 (cn_3) }
% 145.69/18.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c)))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.94 = { by axiom 1 (ifeq_axiom) }
% 145.69/18.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c)))), implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.95 = { by axiom 5 (cn_1) }
% 145.69/18.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.96 = { by axiom 1 (ifeq_axiom) }
% 145.69/18.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(b, c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.97 = { by axiom 4 (condensed_detachment) }
% 145.69/18.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.98 = { by axiom 1 (ifeq_axiom) }
% 145.69/18.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 145.69/18.99 = { by axiom 1 (ifeq_axiom) R->L }
% 145.69/18.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.00 = { by axiom 4 (condensed_detachment) R->L }
% 146.51/19.01 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(is_a_theorem(implies(implies(b, c), implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.01 = { by axiom 2 (cn_3) }
% 146.51/19.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.02 = { by axiom 1 (ifeq_axiom) }
% 146.51/19.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, is_a_theorem(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.03 = { by axiom 5 (cn_1) }
% 146.51/19.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.03 = { by axiom 1 (ifeq_axiom) }
% 146.51/19.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(b, c)), not(implies(implies(not(c), b), implies(implies(b, c), c)))), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.04 = { by axiom 4 (condensed_detachment) }
% 146.51/19.04 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.04 = { by axiom 1 (ifeq_axiom) }
% 146.51/19.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(not(implies(implies(not(c), b), implies(implies(b, c), c)))), not(implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true, is_a_theorem(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.06 = { by axiom 4 (condensed_detachment) }
% 146.51/19.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.06 = { by axiom 1 (ifeq_axiom) }
% 146.51/19.06 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.07 = { by axiom 1 (ifeq_axiom) R->L }
% 146.51/19.07 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.07 = { by axiom 4 (condensed_detachment) R->L }
% 146.51/19.08 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.08 = { by axiom 1 (ifeq_axiom) R->L }
% 146.51/19.09 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 146.51/19.10 = { by axiom 5 (cn_1) R->L }
% 147.31/19.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.10 = { by axiom 1 (ifeq_axiom) R->L }
% 147.31/19.11 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.11 = { by axiom 5 (cn_1) R->L }
% 147.31/19.12 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.13 = { by axiom 4 (condensed_detachment) }
% 147.31/19.13 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.13 = { by axiom 1 (ifeq_axiom) }
% 147.31/19.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.14 = { by axiom 1 (ifeq_axiom) R->L }
% 147.31/19.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.15 = { by axiom 4 (condensed_detachment) R->L }
% 147.31/19.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.16 = { by axiom 3 (cn_2) }
% 147.31/19.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.16 = { by axiom 1 (ifeq_axiom) }
% 147.31/19.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.17 = { by axiom 5 (cn_1) }
% 147.31/19.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.18 = { by axiom 1 (ifeq_axiom) }
% 147.31/19.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.19 = { by axiom 1 (ifeq_axiom) R->L }
% 147.31/19.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.19 = { by axiom 5 (cn_1) R->L }
% 147.31/19.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.20 = { by axiom 4 (condensed_detachment) }
% 147.31/19.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.20 = { by axiom 1 (ifeq_axiom) }
% 147.31/19.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(not(implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 147.31/19.20 = { by axiom 4 (condensed_detachment) }
% 148.12/19.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.21 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.21 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.21 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.21 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.21 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.21 = { by axiom 5 (cn_1) }
% 148.12/19.21 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.21 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 5 (cn_1) }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 4 (condensed_detachment) }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.22 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.22 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 5 (cn_1) R->L }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 5 (cn_1) R->L }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(implies(b, c), c))), implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 4 (condensed_detachment) }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.23 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.24 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.24 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.24 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true, ifeq(is_a_theorem(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c))), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.24 = { by axiom 3 (cn_2) }
% 148.12/19.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true, ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.25 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.25 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.25 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.26 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.26 = { by axiom 5 (cn_1) R->L }
% 148.12/19.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(not(implies(not(c), b)), implies(c, c))), implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.26 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(not(implies(not(c), b)), implies(c, c))), implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.27 = { by axiom 2 (cn_3) R->L }
% 148.12/19.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(not(implies(not(c), b)), implies(c, c))), implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(not(implies(not(c), b)), implies(c, c)))), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))), implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.27 = { by axiom 4 (condensed_detachment) }
% 148.12/19.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.27 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.28 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.29 = { by axiom 4 (condensed_detachment) R->L }
% 148.12/19.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, c), implies(not(implies(c, c)), not(implies(not(c), b))))), true, ifeq(is_a_theorem(implies(c, c)), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.29 = { by axiom 2 (cn_3) }
% 148.12/19.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(c, c)), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.29 = { by axiom 1 (ifeq_axiom) }
% 148.12/19.29 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(c, c)), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.30 = { by axiom 1 (ifeq_axiom) R->L }
% 148.12/19.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.12/19.30 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(c, c)))), true, ifeq(is_a_theorem(implies(c, implies(not(c), c))), true, is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true), true), true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.30 = { by axiom 2 (cn_3) }
% 148.88/19.30 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(c, c)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true), true), true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.31 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, implies(not(c), c)), implies(implies(implies(not(c), c), c), implies(c, c)))), true, is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true), true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.31 = { by axiom 5 (cn_1) }
% 148.88/19.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true), true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.31 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true, is_a_theorem(implies(c, c)), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.31 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true, ifeq(true, true, is_a_theorem(implies(c, c)), true), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.32 = { by axiom 3 (cn_2) R->L }
% 148.88/19.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(c, c))), true, ifeq(is_a_theorem(implies(implies(not(c), c), c)), true, is_a_theorem(implies(c, c)), true), true), true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.32 = { by axiom 4 (condensed_detachment) }
% 148.88/19.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.32 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.32 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.33 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.33 = { by axiom 5 (cn_1) R->L }
% 148.88/19.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(c, c)), not(implies(not(c), b))), implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c))))), true, ifeq(is_a_theorem(implies(not(implies(c, c)), not(implies(not(c), b)))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(c, c)), implies(not(implies(c, c)), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.33 = { by axiom 4 (condensed_detachment) }
% 148.88/19.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.33 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.33 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 5 (cn_1) R->L }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c))), implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c))))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(not(implies(c, c)), implies(c, c)))), true, is_a_theorem(implies(implies(implies(not(implies(c, c)), implies(c, c)), implies(c, c)), implies(implies(not(c), b), implies(c, c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 4 (condensed_detachment) }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(c, c))), true), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(c, c))), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(c, c))), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 5 (cn_1) R->L }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(c, c)), implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c))))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(c, c))), true, is_a_theorem(implies(implies(implies(c, c), implies(implies(not(c), c), c)), implies(implies(not(c), b), implies(implies(not(c), c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.34 = { by axiom 4 (condensed_detachment) }
% 148.88/19.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 5 (cn_1) R->L }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(implies(c, c), implies(implies(not(c), c), c)))), true, is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(implies(c, c), implies(implies(not(c), c), c)))), true, ifeq(true, true, is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 3 (cn_2) R->L }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), c), c), implies(implies(c, c), implies(implies(not(c), c), c)))), true, ifeq(is_a_theorem(implies(implies(not(c), c), c)), true, is_a_theorem(implies(implies(c, c), implies(implies(not(c), c), c))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 4 (condensed_detachment) }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.35 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.35 = { by axiom 5 (cn_1) R->L }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(not(c), c), c)), implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), c), c))), true, is_a_theorem(implies(implies(implies(implies(not(c), c), c), implies(implies(b, c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 4 (condensed_detachment) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), implies(not(c), c))), implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), implies(not(c), c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 5 (cn_1) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), implies(not(c), c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), implies(not(c), c)))), true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 5 (cn_1) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c))), implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(b, c), implies(not(c), c)), implies(implies(not(c), b), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(not(c), b), implies(implies(not(c), b), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 4 (condensed_detachment) }
% 148.88/19.36 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.36 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.36 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.36 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(not(c), b)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(not(c), b))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 3 (cn_2) }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(not(c), b)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(not(c), b)), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c))))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 5 (cn_1) }
% 148.88/19.37 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.37 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 5 (cn_1) R->L }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c))), implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))), implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 4 (condensed_detachment) }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.38 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.39 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))), implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.39 = { by axiom 5 (cn_1) }
% 148.88/19.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.39 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.39 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.39 = { by axiom 4 (condensed_detachment) R->L }
% 148.88/19.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(b, b)), not(not(implies(not(c), b)))), implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.40 = { by axiom 5 (cn_1) }
% 148.88/19.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.40 = { by axiom 1 (ifeq_axiom) }
% 148.88/19.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 148.88/19.40 = { by axiom 1 (ifeq_axiom) R->L }
% 148.88/19.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.41 = { by axiom 4 (condensed_detachment) R->L }
% 149.73/19.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.41 = { by axiom 3 (cn_2) }
% 149.73/19.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, ifeq(true, true, is_a_theorem(implies(b, b)), true), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.41 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.41 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.42 = { by axiom 5 (cn_1) R->L }
% 149.73/19.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.42 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.42 = { by axiom 2 (cn_3) R->L }
% 149.73/19.42 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(b, b)))), true, ifeq(is_a_theorem(implies(b, implies(not(b), b))), true, is_a_theorem(implies(implies(implies(not(b), b), b), implies(b, b))), true), true), true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.43 = { by axiom 4 (condensed_detachment) }
% 149.73/19.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, b)), true), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.43 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.43 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.43 = { by axiom 2 (cn_3) R->L }
% 149.73/19.43 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(not(implies(b, b)), not(not(implies(not(c), b)))))), true, ifeq(is_a_theorem(implies(b, b)), true, is_a_theorem(implies(not(implies(b, b)), not(not(implies(not(c), b))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.44 = { by axiom 4 (condensed_detachment) }
% 149.73/19.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.44 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.44 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.45 = { by axiom 4 (condensed_detachment) R->L }
% 149.73/19.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(not(not(implies(not(c), b))), implies(b, b))), implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(is_a_theorem(implies(not(implies(not(c), b)), implies(not(not(implies(not(c), b))), implies(b, b)))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.45 = { by axiom 2 (cn_3) }
% 149.73/19.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(not(not(implies(not(c), b))), implies(b, b))), implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.45 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(not(not(implies(not(c), b))), implies(b, b))), implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.45 = { by axiom 5 (cn_1) }
% 149.73/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.46 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b))), implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(c), b))), implies(b, b)), implies(not(implies(b, b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(not(implies(b, b)), implies(b, b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.46 = { by axiom 4 (condensed_detachment) }
% 149.73/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.46 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.46 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 3 (cn_2) R->L }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b)), implies(not(implies(not(c), b)), implies(b, b)))), true, ifeq(is_a_theorem(implies(implies(not(implies(b, b)), implies(b, b)), implies(b, b))), true, is_a_theorem(implies(not(implies(not(c), b)), implies(b, b))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 4 (condensed_detachment) }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, ifeq(true, true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 4 (condensed_detachment) R->L }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(b, b), implies(not(c), b))), implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true, ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 5 (cn_1) }
% 149.73/19.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.47 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.48 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.48 = { by axiom 4 (condensed_detachment) R->L }
% 149.73/19.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.48 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.48 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.49 = { by axiom 5 (cn_1) R->L }
% 149.73/19.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.49 = { by axiom 1 (ifeq_axiom) R->L }
% 149.73/19.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.49 = { by axiom 5 (cn_1) R->L }
% 149.73/19.49 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(not(c), b))), implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))))), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(implies(not(b), b), b), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))), implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.49 = { by axiom 4 (condensed_detachment) }
% 149.73/19.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.50 = { by axiom 1 (ifeq_axiom) }
% 149.73/19.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 149.73/19.50 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.50 = { by axiom 4 (condensed_detachment) R->L }
% 150.48/19.50 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(is_a_theorem(implies(implies(not(b), b), b)), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.50 = { by axiom 3 (cn_2) }
% 150.48/19.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.51 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), b), b), implies(implies(b, b), implies(implies(not(b), b), b)))), true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.51 = { by axiom 5 (cn_1) }
% 150.48/19.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.51 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.51 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.52 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.52 = { by axiom 5 (cn_1) R->L }
% 150.48/19.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, b), implies(implies(not(b), b), b)), implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b))))), true, ifeq(is_a_theorem(implies(implies(b, b), implies(implies(not(b), b), b))), true, is_a_theorem(implies(implies(implies(implies(not(b), b), b), implies(not(c), b)), implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.52 = { by axiom 4 (condensed_detachment) }
% 150.48/19.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.52 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.52 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.52 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.53 = { by axiom 4 (condensed_detachment) R->L }
% 150.48/19.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(c), implies(not(b), b))), implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b)))))), true, ifeq(is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.53 = { by axiom 5 (cn_1) }
% 150.48/19.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.53 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.53 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.54 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.54 = { by axiom 4 (condensed_detachment) R->L }
% 150.48/19.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(implies(not(not(c)), b), implies(not(b), b))), implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b)))))), true, ifeq(is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.54 = { by axiom 5 (cn_1) }
% 150.48/19.54 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.55 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.55 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.55 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.55 = { by axiom 5 (cn_1) R->L }
% 150.48/19.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.56 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.56 = { by axiom 4 (condensed_detachment) R->L }
% 150.48/19.56 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(not(c)))), implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))))), true, ifeq(is_a_theorem(implies(b, implies(not(b), not(not(c))))), true, is_a_theorem(implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.57 = { by axiom 2 (cn_3) }
% 150.48/19.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(not(c)))), implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.57 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), not(not(c)))), implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))))), true, is_a_theorem(implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.57 = { by axiom 5 (cn_1) }
% 150.48/19.57 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.58 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b))), implies(b, implies(implies(not(not(c)), b), implies(not(b), b))))), true, ifeq(is_a_theorem(implies(implies(not(b), not(not(c))), implies(implies(not(not(c)), b), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(implies(not(not(c)), b), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.58 = { by axiom 4 (condensed_detachment) }
% 150.48/19.58 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.58 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.59 = { by axiom 1 (ifeq_axiom) R->L }
% 150.48/19.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(true, true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.59 = { by axiom 4 (condensed_detachment) R->L }
% 150.48/19.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(c), implies(not(not(c)), b)), implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))))), true, ifeq(is_a_theorem(implies(not(c), implies(not(not(c)), b))), true, is_a_theorem(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.59 = { by axiom 2 (cn_3) }
% 150.48/19.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(c), implies(not(not(c)), b)), implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.60 = { by axiom 1 (ifeq_axiom) }
% 150.48/19.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(c), implies(not(not(c)), b)), implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))))), true, is_a_theorem(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 150.48/19.60 = { by axiom 5 (cn_1) }
% 151.27/19.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b)))), true), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.60 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b))), implies(b, implies(not(c), implies(not(b), b))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(c)), b), implies(not(b), b)), implies(not(c), implies(not(b), b)))), true, is_a_theorem(implies(b, implies(not(c), implies(not(b), b)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.60 = { by axiom 4 (condensed_detachment) }
% 151.27/19.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.61 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b))), implies(b, implies(implies(b, b), implies(not(c), b))))), true, ifeq(is_a_theorem(implies(implies(not(c), implies(not(b), b)), implies(implies(b, b), implies(not(c), b)))), true, is_a_theorem(implies(b, implies(implies(b, b), implies(not(c), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.61 = { by axiom 4 (condensed_detachment) }
% 151.27/19.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.61 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.61 = { by axiom 1 (ifeq_axiom) R->L }
% 151.27/19.61 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.61 = { by axiom 4 (condensed_detachment) R->L }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.62 = { by axiom 5 (cn_1) }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.62 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.62 = { by axiom 5 (cn_1) }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.62 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, b), implies(not(c), b)), implies(not(implies(not(c), b)), implies(not(c), b))), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true, is_a_theorem(implies(implies(not(implies(not(c), b)), implies(b, b)), implies(b, implies(not(implies(not(c), b)), implies(not(c), b))))), true), true), true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.62 = { by axiom 4 (condensed_detachment) }
% 151.27/19.62 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) R->L }
% 151.27/19.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 5 (cn_1) R->L }
% 151.27/19.63 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(implies(not(c), b)), implies(not(c), b))), implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c))))), true, ifeq(is_a_theorem(implies(b, implies(not(implies(not(c), b)), implies(not(c), b)))), true, is_a_theorem(implies(implies(implies(not(implies(not(c), b)), implies(not(c), b)), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true), true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 4 (condensed_detachment) }
% 151.27/19.63 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.63 ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(c), b), implies(implies(b, c), c)), implies(b, implies(implies(b, c), c)))), true, ifeq(is_a_theorem(implies(implies(not(c), b), implies(implies(b, c), c))), true, is_a_theorem(implies(b, implies(implies(b, c), c))), true), true), true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 4 (condensed_detachment) }
% 151.27/19.63 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.63 ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) R->L }
% 151.27/19.63 ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 4 (condensed_detachment) R->L }
% 151.27/19.63 ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), c), implies(a, c))), implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c)))))), true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 5 (cn_1) }
% 151.27/19.63 ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.63 ifeq(ifeq(is_a_theorem(implies(implies(a, implies(b, c)), implies(implies(implies(b, c), c), implies(a, c)))), true, is_a_theorem(implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 5 (cn_1) }
% 151.27/19.63 ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 1 (ifeq_axiom) }
% 151.27/19.63 ifeq(is_a_theorem(implies(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c))), implies(implies(a, implies(b, c)), implies(b, implies(a, c))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(b, c), c), implies(a, c)), implies(b, implies(a, c)))), true, is_a_theorem(implies(implies(a, implies(b, c)), implies(b, implies(a, c)))), true), true)
% 151.27/19.63 = { by axiom 4 (condensed_detachment) }
% 151.27/19.63 true
% 151.27/19.63 % SZS output end Proof
% 151.27/19.63
% 151.27/19.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------