%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:01 AM UTC 2026
% Result : Unsatisfiable 9.61s 1.69s
% Output : Proof 85.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n012.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sun Sep 27 15:21:19 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.61/1.69 Command-line arguments: --no-flatten-goal
% 9.61/1.69
% 9.61/1.69 % SZS status Unsatisfiable
% 9.61/1.69
% 54.66/8.22 % SZS output start Proof
% 54.66/8.22 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 54.66/8.22 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 54.66/8.22 Axiom 3 (lg_2): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), W), W)) = true.
% 54.66/8.22 Axiom 4 (lg_4): is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), W), equivalent(equivalent(equivalent(X, V), Z), equivalent(equivalent(Y, V), W)))) = true.
% 54.66/8.29 Axiom 5 (lg_3): is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), W), equivalent(equivalent(Y, Z), W)), V), V)) = true.
% 54.66/8.29
% 54.66/8.29 Goal 1 (prove_lg_1): is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)) = true.
% 54.66/8.29 Proof:
% 54.66/8.29 is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))
% 54.66/8.29 = { by axiom 1 (ifeq_axiom) R->L }
% 54.66/8.29 ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.31 = { by axiom 2 (condensed_detachment) R->L }
% 55.37/8.31 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.31 = { by axiom 1 (ifeq_axiom) R->L }
% 55.37/8.31 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.32 = { by axiom 2 (condensed_detachment) R->L }
% 55.37/8.32 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.32 = { by axiom 3 (lg_2) }
% 55.37/8.33 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.33 = { by axiom 1 (ifeq_axiom) }
% 55.37/8.33 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.33 = { by axiom 4 (lg_4) }
% 55.37/8.33 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.33 = { by axiom 1 (ifeq_axiom) }
% 55.37/8.34 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.34 = { by axiom 1 (ifeq_axiom) R->L }
% 55.37/8.34 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.34 = { by axiom 3 (lg_2) R->L }
% 55.37/8.34 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.34 = { by axiom 2 (condensed_detachment) }
% 55.37/8.34 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.34 = { by axiom 1 (ifeq_axiom) }
% 55.37/8.34 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.34 = { by axiom 1 (ifeq_axiom) R->L }
% 55.37/8.34 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.35 = { by axiom 2 (condensed_detachment) R->L }
% 55.37/8.35 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.36 = { by axiom 1 (ifeq_axiom) R->L }
% 55.37/8.36 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.37 = { by axiom 5 (lg_3) R->L }
% 55.37/8.38 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 55.37/8.39 = { by axiom 1 (ifeq_axiom) R->L }
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% 56.11/8.41 = { by axiom 2 (condensed_detachment) R->L }
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% 56.11/8.43 = { by axiom 1 (ifeq_axiom) R->L }
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% 56.11/8.44 = { by axiom 4 (lg_4) R->L }
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% 56.11/8.46 = { by axiom 1 (ifeq_axiom) R->L }
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% 56.11/8.49 = { by axiom 2 (condensed_detachment) }
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% 56.78/8.50 = { by axiom 1 (ifeq_axiom) }
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% 56.78/8.51 = { by axiom 1 (ifeq_axiom) R->L }
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% 56.78/8.52 = { by axiom 4 (lg_4) R->L }
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% 56.78/8.53 = { by axiom 1 (ifeq_axiom) R->L }
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% 56.78/8.54 = { by axiom 3 (lg_2) R->L }
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% 56.78/8.54 = { by axiom 2 (condensed_detachment) }
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is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.55 = { by axiom 2 (condensed_detachment) }
% 56.78/8.55 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.55 = { by axiom 1 (ifeq_axiom) }
% 56.78/8.55 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.55 = { by axiom 1 (ifeq_axiom) R->L }
% 56.78/8.55 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.56 = { by axiom 3 (lg_2) R->L }
% 56.78/8.56 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.57 = { by axiom 1 (ifeq_axiom) R->L }
% 56.78/8.57 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 56.78/8.58 = { by axiom 2 (condensed_detachment) R->L }
% 56.78/8.59 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), 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equivalent(equivalent(a, equivalent(b, b)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), 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equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), 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equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, 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% 56.78/8.60 = { by axiom 1 (ifeq_axiom) R->L }
% 56.78/8.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), 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equivalent(equivalent(a, equivalent(b, b)), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), 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% 57.50/8.61 = { by axiom 2 (condensed_detachment) R->L }
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% 58.91/8.83 = { by axiom 5 (lg_3) }
% 58.91/8.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.84 = { by axiom 1 (ifeq_axiom) }
% 58.91/8.84 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(b, b))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.84 = { by axiom 2 (condensed_detachment) }
% 58.91/8.84 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.84 = { by axiom 1 (ifeq_axiom) }
% 58.91/8.84 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.84 = { by axiom 1 (ifeq_axiom) R->L }
% 58.91/8.84 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.84 = { by axiom 2 (condensed_detachment) R->L }
% 58.91/8.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.85 = { by axiom 1 (ifeq_axiom) R->L }
% 58.91/8.85 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 58.91/8.86 = { by axiom 2 (condensed_detachment) R->L }
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% 58.91/8.87 = { by axiom 1 (ifeq_axiom) R->L }
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% 58.91/8.87 = { by axiom 2 (condensed_detachment) R->L }
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% 58.91/8.89 = { by axiom 3 (lg_2) }
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% 59.61/8.91 = { by axiom 1 (ifeq_axiom) }
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% 59.61/8.99 = { by axiom 4 (lg_4) }
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% 60.46/9.07 = { by axiom 1 (ifeq_axiom) }
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% 61.15/9.12 = { by axiom 1 (ifeq_axiom) R->L }
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% 62.41/9.38 = { by axiom 2 (condensed_detachment) }
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% 63.11/9.41 = { by axiom 1 (ifeq_axiom) }
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% 63.11/9.43 = { by axiom 1 (ifeq_axiom) R->L }
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% 63.11/9.45 = { by axiom 2 (condensed_detachment) R->L }
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% 63.11/9.48 = { by axiom 1 (ifeq_axiom) R->L }
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% 63.82/9.51 = { by axiom 4 (lg_4) R->L }
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% 63.82/9.53 = { by axiom 1 (ifeq_axiom) R->L }
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% 63.82/9.56 = { by axiom 3 (lg_2) R->L }
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% 63.82/9.59 = { by axiom 2 (condensed_detachment) }
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% 64.52/9.61 = { by axiom 1 (ifeq_axiom) }
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% 64.52/9.63 = { by axiom 1 (ifeq_axiom) R->L }
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% 64.52/9.65 = { by axiom 4 (lg_4) R->L }
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% 64.52/9.67 = { by axiom 1 (ifeq_axiom) R->L }
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% 64.52/9.69 = { by axiom 3 (lg_2) R->L }
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% 65.22/9.72 = { by axiom 1 (ifeq_axiom) }
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% 67.56/10.05 = { by axiom 1 (ifeq_axiom) R->L }
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% 67.56/10.07 = { by axiom 4 (lg_4) R->L }
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% 67.56/10.09 = { by axiom 1 (ifeq_axiom) R->L }
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% 67.56/10.11 = { by axiom 3 (lg_2) R->L }
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% 68.27/10.14 = { by axiom 2 (condensed_detachment) }
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% 68.27/10.15 = { by axiom 1 (ifeq_axiom) }
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% 68.27/10.17 = { by axiom 1 (ifeq_axiom) R->L }
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% 68.27/10.18 = { by axiom 3 (lg_2) R->L }
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% 68.27/10.19 = { by axiom 2 (condensed_detachment) }
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% 68.75/10.20 = { by axiom 1 (ifeq_axiom) }
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% 68.75/10.21 = { by axiom 1 (ifeq_axiom) R->L }
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% 68.75/10.23 = { by axiom 2 (condensed_detachment) R->L }
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% 68.75/10.25 = { by axiom 1 (ifeq_axiom) R->L }
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% 68.75/10.27 = { by axiom 4 (lg_4) R->L }
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% 68.75/10.28 = { by axiom 1 (ifeq_axiom) R->L }
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% 68.75/10.30 = { by axiom 3 (lg_2) R->L }
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% 69.46/10.32 = { by axiom 2 (condensed_detachment) }
% 69.46/10.32 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, b), X2), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(S, b), X2), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.33 = { by axiom 1 (ifeq_axiom) }
% 69.46/10.33 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(S, b), X2), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(S, b), X2), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.34 = { by axiom 4 (lg_4) }
% 69.46/10.34 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.34 = { by axiom 1 (ifeq_axiom) }
% 69.46/10.35 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.35 = { by axiom 2 (condensed_detachment) }
% 69.46/10.35 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.36 = { by axiom 1 (ifeq_axiom) }
% 69.46/10.37 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 69.46/10.39 = { by axiom 1 (ifeq_axiom) R->L }
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% 70.16/10.43 = { by axiom 2 (condensed_detachment) R->L }
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% 84.93/12.59 = { by axiom 2 (condensed_detachment) }
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% 84.93/12.60 = { by axiom 1 (ifeq_axiom) }
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% 85.62/12.60 = { by axiom 4 (lg_4) }
% 85.62/12.60 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.61 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.61 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.61 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.61 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.61 = { by axiom 3 (lg_2) R->L }
% 85.62/12.62 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(b, b), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.62 = { by axiom 2 (condensed_detachment) }
% 85.62/12.62 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.62 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.62 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, b), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), c), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.62 = { by axiom 2 (condensed_detachment) }
% 85.62/12.62 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.62 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.62 ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true)
% 85.62/12.62 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.62 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 2 (condensed_detachment) R->L }
% 85.62/12.62 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.62 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 4 (lg_4) R->L }
% 85.62/12.62 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.62 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 3 (lg_2) R->L }
% 85.62/12.62 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c)), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.62 = { by axiom 2 (condensed_detachment) }
% 85.62/12.62 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.63 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.63 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 2 (condensed_detachment) R->L }
% 85.62/12.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 3 (lg_2) }
% 85.62/12.63 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.63 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.63 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.63 = { by axiom 4 (lg_4) R->L }
% 85.62/12.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 3 (lg_2) R->L }
% 85.62/12.64 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(a, equivalent(b, b))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(b, b), equivalent(b, b))), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 2 (condensed_detachment) }
% 85.62/12.64 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.64 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.64 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.64 = { by axiom 2 (condensed_detachment) R->L }
% 85.62/12.65 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.65 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.65 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.65 = { by axiom 4 (lg_4) R->L }
% 85.62/12.66 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.66 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.66 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.66 = { by axiom 3 (lg_2) R->L }
% 85.62/12.66 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.66 = { by axiom 2 (condensed_detachment) }
% 85.62/12.66 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.66 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.66 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.67 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.67 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.67 = { by axiom 2 (condensed_detachment) R->L }
% 85.62/12.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.67 = { by axiom 3 (lg_2) }
% 85.62/12.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.67 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.67 = { by axiom 4 (lg_4) }
% 85.62/12.67 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.68 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 1 (ifeq_axiom) R->L }
% 85.62/12.68 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 3 (lg_2) R->L }
% 85.62/12.68 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(b, b), V2)), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), V2), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 2 (condensed_detachment) }
% 85.62/12.68 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.68 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(b, b), equivalent(b, b)), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, b)), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(a, equivalent(b, b)), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 2 (condensed_detachment) }
% 85.62/12.68 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 1 (ifeq_axiom) }
% 85.62/12.68 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), equivalent(equivalent(equivalent(b, b), a), equivalent(equivalent(a, equivalent(b, b)), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, b), a)), c), c)), true), true)
% 85.62/12.68 = { by axiom 2 (condensed_detachment) }
% 85.62/12.68 true
% 85.62/12.68 % SZS output end Proof
% 85.62/12.68
% 85.62/12.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------