%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 11:48:49 AM UTC 2026
% Result : Unsatisfiable 2.97s 0.82s
% Output : Proof 5.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 15:16:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.97/0.82 Command-line arguments: --flatten-regeneralise
% 2.97/0.82
% 2.97/0.82 % SZS status Unsatisfiable
% 2.97/0.82
% 4.98/1.10 % SZS output start Proof
% 4.98/1.10 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 4.98/1.10 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.
% 4.98/1.11 Axiom 3 (yqf): is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(X, Z), equivalent(Z, Y)))) = true.
% 4.98/1.11
% 4.98/1.11 Goal 1 (prove_yql): is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))) = true.
% 4.98/1.11 Proof:
% 4.98/1.11 is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))
% 4.98/1.11 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.11 ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.11 = { by axiom 2 (condensed_detachment) R->L }
% 4.98/1.11 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.11 = { by axiom 3 (yqf) }
% 4.98/1.11 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.12 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.12 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 2 (condensed_detachment) R->L }
% 4.98/1.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 2 (condensed_detachment) R->L }
% 4.98/1.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))))), true, ifeq(is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 3 (yqf) }
% 4.98/1.12 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.12 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 3 (yqf) }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 3 (yqf) R->L }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true, ifeq(is_a_theorem(equivalent(equivalent(X, X), equivalent(equivalent(X, X), equivalent(X, X)))), true, is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 2 (condensed_detachment) }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.13 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.13 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.14 = { by axiom 2 (condensed_detachment) R->L }
% 4.98/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.14 = { by axiom 1 (ifeq_axiom) R->L }
% 4.98/1.14 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.15 = { by axiom 2 (condensed_detachment) R->L }
% 4.98/1.15 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.15 = { by axiom 3 (yqf) }
% 4.98/1.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.16 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.16 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.16 = { by axiom 3 (yqf) }
% 4.98/1.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.17 = { by axiom 1 (ifeq_axiom) }
% 4.98/1.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 4.98/1.17 = { by axiom 1 (ifeq_axiom) R->L }
% 5.72/1.17 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.17 = { by axiom 3 (yqf) R->L }
% 5.72/1.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(a, b), equivalent(a, b))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.18 = { by axiom 2 (condensed_detachment) }
% 5.72/1.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.18 = { by axiom 1 (ifeq_axiom) }
% 5.72/1.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.18 = { by axiom 1 (ifeq_axiom) R->L }
% 5.72/1.18 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.18 = { by axiom 2 (condensed_detachment) R->L }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.19 = { by axiom 3 (yqf) }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.19 = { by axiom 1 (ifeq_axiom) }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.19 = { by axiom 3 (yqf) }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.19 = { by axiom 1 (ifeq_axiom) }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.19 = { by axiom 1 (ifeq_axiom) R->L }
% 5.72/1.19 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.72/1.20 = { by axiom 3 (yqf) R->L }
% 5.72/1.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(a, b))), equivalent(equivalent(equivalent(X, X), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(a, b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 2 (condensed_detachment) }
% 5.87/1.20 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.20 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.20 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 3 (yqf) R->L }
% 5.87/1.20 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X)))), equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, X), equivalent(X, X)), equivalent(equivalent(X, X), equivalent(X, X))), equivalent(equivalent(a, b), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 2 (condensed_detachment) }
% 5.87/1.20 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.20 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.20 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 3 (yqf) R->L }
% 5.87/1.20 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(a, b)), equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, b), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(equivalent(a, c), equivalent(c, b))), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.20 = { by axiom 2 (condensed_detachment) }
% 5.87/1.20 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.21 ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.21 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.21 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 3 (yqf) }
% 5.87/1.21 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.21 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.21 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))))), true, ifeq(is_a_theorem(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 3 (yqf) }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.21 = { by axiom 3 (yqf) }
% 5.87/1.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 3 (yqf) R->L }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true, ifeq(is_a_theorem(equivalent(equivalent(Y, Y), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true, is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 2 (condensed_detachment) }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.22 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.22 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.23 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.23 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.23 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.23 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.24 = { by axiom 3 (yqf) }
% 5.87/1.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.24 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.24 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.25 = { by axiom 3 (yqf) }
% 5.87/1.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.25 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.25 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.25 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.26 = { by axiom 3 (yqf) R->L }
% 5.87/1.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(a, c), equivalent(a, c))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.26 = { by axiom 2 (condensed_detachment) }
% 5.87/1.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.26 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.26 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.26 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.27 = { by axiom 2 (condensed_detachment) R->L }
% 5.87/1.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.27 = { by axiom 3 (yqf) }
% 5.87/1.27 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.27 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 3 (yqf) }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 3 (yqf) R->L }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(a, c))), equivalent(equivalent(equivalent(Y, Y), equivalent(a, c)), equivalent(equivalent(a, c), equivalent(a, c))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 2 (condensed_detachment) }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.28 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.28 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.29 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 3 (yqf) R->L }
% 5.87/1.29 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y)))), equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(Y, Y), equivalent(Y, Y)), equivalent(equivalent(Y, Y), equivalent(Y, Y))), equivalent(equivalent(a, c), equivalent(a, c)))), true), true), true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 2 (condensed_detachment) }
% 5.87/1.29 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.29 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 1 (ifeq_axiom) R->L }
% 5.87/1.29 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 3 (yqf) R->L }
% 5.87/1.29 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(a, c)), equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, c), equivalent(a, c))), true, is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(equivalent(c, b), equivalent(a, c)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 2 (condensed_detachment) }
% 5.87/1.29 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 1 (ifeq_axiom) }
% 5.87/1.29 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b)), equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, c), equivalent(c, b)), equivalent(a, b))), true, is_a_theorem(equivalent(equivalent(a, b), equivalent(equivalent(c, b), equivalent(a, c)))), true), true)
% 5.87/1.29 = { by axiom 2 (condensed_detachment) }
% 5.87/1.29 true
% 5.87/1.29 % SZS output end Proof
% 5.87/1.29
% 5.87/1.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------