%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:51 AM UTC 2026
% Result : Unsatisfiable 3.88s 0.96s
% Output : Proof 5.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 15:19:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/0.96 Command-line arguments: --flatten-regeneralise
% 3.88/0.96
% 3.88/0.96 % SZS status Unsatisfiable
% 3.88/0.96
% 4.30/1.14 % SZS output start Proof
% 4.30/1.14 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.30/1.14 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.
% 4.84/1.14 Axiom 3 (yql): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z)))) = true.
% 4.84/1.14
% 4.84/1.14 Goal 1 (prove_ec_2): is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))) = true.
% 4.84/1.14 Proof:
% 4.84/1.14 is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))
% 4.84/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.14 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true)
% 4.84/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.14 ifeq(true, true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.14 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 3 (yql) }
% 4.84/1.14 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.14 ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.14 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.14 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 3 (yql) R->L }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 3 (yql) R->L }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X))), equivalent(equivalent(b, c), equivalent(b, c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 2 (condensed_detachment) }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(equivalent(X, c), equivalent(b, X)))), true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 3 (yql) }
% 4.84/1.15 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.15 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.15 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 3 (yql) R->L }
% 4.84/1.15 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), equivalent(b, c)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(b, c), equivalent(b, c))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 2 (condensed_detachment) }
% 4.84/1.15 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.15 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.15 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 3 (yql) }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 3 (yql) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.16 = { by axiom 3 (yql) }
% 4.84/1.16 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 3 (yql) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(Y, a), equivalent(equivalent(b, c), Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 2 (condensed_detachment) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 3 (yql) }
% 4.84/1.17 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.18 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.18 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.18 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.18 = { by axiom 3 (yql) R->L }
% 4.84/1.18 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.18 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.18 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.18 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.18 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.18 = { by axiom 3 (yql) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 3 (yql) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(Z, equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), Z)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 2 (condensed_detachment) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.19 = { by axiom 2 (condensed_detachment) }
% 4.84/1.19 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.20 = { by axiom 1 (ifeq_axiom) }
% 4.84/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 4.84/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.20 = { by axiom 2 (condensed_detachment) R->L }
% 4.84/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 4.84/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 3 (yql) R->L }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 3 (yql) R->L }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))), equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 2 (condensed_detachment) }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 1 (ifeq_axiom) }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 5.20/1.20 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 3 (yql) R->L }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 3 (yql) R->L }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(equivalent(b, c), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))), equivalent(equivalent(a, c), equivalent(equivalent(a, b), a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 2 (condensed_detachment) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 2 (condensed_detachment) R->L }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 3 (yql) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 3 (yql) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b)))), equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(equivalent(a, b), a), equivalent(equivalent(b, c), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, c), a), equivalent(equivalent(a, b), c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 2 (condensed_detachment) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.20/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a)), equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(equivalent(b, c), a))), true, is_a_theorem(equivalent(equivalent(a, equivalent(b, c)), equivalent(equivalent(a, b), c))), true), true)
% 5.20/1.21 = { by axiom 2 (condensed_detachment) }
% 5.20/1.21 true
% 5.20/1.21 % SZS output end Proof
% 5.20/1.21
% 5.20/1.21 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------