%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:49:02 AM UTC 2026
% Result : Unsatisfiable 16.10s 2.54s
% Output : Proof 28.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 15:23:40 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.10/2.54 Command-line arguments: --no-flatten-goal
% 16.10/2.54
% 16.10/2.54 % SZS status Unsatisfiable
% 16.10/2.54
% 21.44/3.20 % SZS output start Proof
% 21.44/3.20 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 21.44/3.20 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.
% 21.44/3.20 Axiom 3 (q_3): is_a_theorem(equivalent(equivalent(equivalent(X, Y), equivalent(equivalent(Y, X), Z)), Z)) = true.
% 21.62/3.21 Axiom 4 (p_4): is_a_theorem(equivalent(X, equivalent(equivalent(equivalent(equivalent(Y, Z), equivalent(Y, W)), equivalent(Z, W)), X))) = true.
% 21.62/3.21
% 21.62/3.21 Goal 1 (prove_p_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))) = true.
% 21.62/3.21 Proof:
% 21.62/3.21 is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))
% 21.62/3.22 = { by axiom 1 (ifeq_axiom) R->L }
% 21.62/3.22 ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.22 = { by axiom 2 (condensed_detachment) R->L }
% 21.62/3.22 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.22 = { by axiom 1 (ifeq_axiom) R->L }
% 21.62/3.22 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.23 = { by axiom 2 (condensed_detachment) R->L }
% 21.62/3.23 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.24 = { by axiom 1 (ifeq_axiom) R->L }
% 21.62/3.24 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.26 = { by axiom 3 (q_3) R->L }
% 21.62/3.26 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.27 = { by axiom 1 (ifeq_axiom) R->L }
% 21.62/3.28 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 21.62/3.29 = { by axiom 2 (condensed_detachment) R->L }
% 22.44/3.31 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), 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b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), 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% 22.44/3.32 = { by axiom 3 (q_3) }
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% 22.44/3.34 = { by axiom 1 (ifeq_axiom) }
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% 22.44/3.35 = { by axiom 4 (p_4) }
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% 22.44/3.36 = { by axiom 1 (ifeq_axiom) }
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% 22.44/3.37 = { by axiom 2 (condensed_detachment) }
% 22.44/3.37 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 22.44/3.38 = { by axiom 1 (ifeq_axiom) }
% 22.44/3.38 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 22.44/3.38 = { by axiom 1 (ifeq_axiom) R->L }
% 22.44/3.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 22.44/3.39 = { by axiom 2 (condensed_detachment) R->L }
% 22.44/3.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 22.44/3.40 = { by axiom 3 (q_3) }
% 22.44/3.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 22.44/3.40 = { by axiom 1 (ifeq_axiom) }
% 23.18/3.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.41 = { by axiom 4 (p_4) }
% 23.18/3.41 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.42 = { by axiom 1 (ifeq_axiom) }
% 23.18/3.42 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.42 = { by axiom 1 (ifeq_axiom) R->L }
% 23.18/3.43 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.43 = { by axiom 2 (condensed_detachment) R->L }
% 23.18/3.44 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), 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equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, 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e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), 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is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.45 = { by axiom 3 (q_3) }
% 23.18/3.45 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), 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b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.46 = { by axiom 1 (ifeq_axiom) }
% 23.18/3.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), 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b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.47 = { by axiom 4 (p_4) }
% 23.18/3.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.47 = { by axiom 1 (ifeq_axiom) }
% 23.18/3.47 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(e, b), equivalent(equivalent(a, e), equivalent(a, b))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.48 = { by axiom 2 (condensed_detachment) }
% 23.18/3.48 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.49 = { by axiom 1 (ifeq_axiom) }
% 23.18/3.49 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.49 = { by axiom 1 (ifeq_axiom) R->L }
% 23.18/3.49 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 23.18/3.50 = { by axiom 2 (condensed_detachment) R->L }
% 24.01/3.51 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.52 = { by axiom 3 (q_3) }
% 24.01/3.52 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.52 = { by axiom 1 (ifeq_axiom) }
% 24.01/3.52 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.52 = { by axiom 4 (p_4) }
% 24.01/3.53 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.53 = { by axiom 1 (ifeq_axiom) }
% 24.01/3.53 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.54 = { by axiom 2 (condensed_detachment) }
% 24.01/3.54 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.54 = { by axiom 1 (ifeq_axiom) }
% 24.01/3.54 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(e, b)), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.54 = { by axiom 4 (p_4) }
% 24.01/3.54 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.54 = { by axiom 1 (ifeq_axiom) }
% 24.01/3.54 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true)
% 24.01/3.55 = { by axiom 1 (ifeq_axiom) R->L }
% 24.01/3.55 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.01/3.55 = { by axiom 2 (condensed_detachment) R->L }
% 24.01/3.55 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.01/3.56 = { by axiom 1 (ifeq_axiom) R->L }
% 24.01/3.56 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 24.01/3.57 = { by axiom 2 (condensed_detachment) R->L }
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% 24.01/3.58 = { by axiom 1 (ifeq_axiom) R->L }
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% 24.77/3.62 = { by axiom 3 (q_3) R->L }
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% 24.77/3.64 = { by axiom 1 (ifeq_axiom) R->L }
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% 24.77/3.67 = { by axiom 2 (condensed_detachment) R->L }
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% 25.59/3.77 = { by axiom 4 (p_4) }
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% 25.59/3.78 = { by axiom 1 (ifeq_axiom) }
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% 25.59/3.79 = { by axiom 2 (condensed_detachment) }
% 25.59/3.79 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.80 = { by axiom 1 (ifeq_axiom) }
% 26.39/3.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.81 = { by axiom 1 (ifeq_axiom) R->L }
% 26.39/3.82 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.82 = { by axiom 2 (condensed_detachment) R->L }
% 26.39/3.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.83 = { by axiom 3 (q_3) }
% 26.39/3.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.85 = { by axiom 1 (ifeq_axiom) }
% 26.39/3.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), 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ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.86 = { by axiom 4 (p_4) }
% 26.39/3.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 26.39/3.88 = { by axiom 1 (ifeq_axiom) }
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% 26.39/3.89 = { by axiom 1 (ifeq_axiom) R->L }
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% 26.39/3.91 = { by axiom 2 (condensed_detachment) R->L }
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% 27.22/3.94 = { by axiom 3 (q_3) }
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% 27.22/3.95 = { by axiom 1 (ifeq_axiom) }
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% 27.22/3.97 = { by axiom 4 (p_4) }
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% 27.22/3.98 = { by axiom 1 (ifeq_axiom) }
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% 27.22/3.99 = { by axiom 2 (condensed_detachment) }
% 27.22/3.99 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.22/4.01 = { by axiom 1 (ifeq_axiom) }
% 27.22/4.01 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.22/4.02 = { by axiom 1 (ifeq_axiom) R->L }
% 27.22/4.02 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.22/4.03 = { by axiom 2 (condensed_detachment) R->L }
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% 27.22/4.06 = { by axiom 3 (q_3) }
% 27.22/4.07 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), 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is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 27.22/4.07 = { by axiom 1 (ifeq_axiom) }
% 27.22/4.08 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.08 = { by axiom 4 (p_4) }
% 28.54/4.09 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.09 = { by axiom 1 (ifeq_axiom) }
% 28.54/4.09 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.10 = { by axiom 2 (condensed_detachment) }
% 28.54/4.10 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.10 = { by axiom 1 (ifeq_axiom) }
% 28.54/4.10 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.10 = { by axiom 4 (p_4) }
% 28.54/4.10 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.10 = { by axiom 1 (ifeq_axiom) }
% 28.54/4.10 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, e), equivalent(a, b)), equivalent(equivalent(a, e), c)), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(e, b), equivalent(equivalent(a, e), c)))), true), true)
% 28.54/4.10 = { by axiom 2 (condensed_detachment) }
% 28.54/4.10 true
% 28.54/4.10 % SZS output end Proof
% 28.54/4.10
% 28.54/4.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------