%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:48:49 AM UTC 2026
% Result : Unsatisfiable 20.42s 3.24s
% Output : Proof 27.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 15:18:26 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.42/3.24 Command-line arguments: --no-flatten-goal
% 20.42/3.24
% 20.42/3.24 % SZS status Unsatisfiable
% 20.42/3.24
% 25.02/3.76 % SZS output start Proof
% 25.02/3.76 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 25.02/3.76 Axiom 2 (ec_4): is_a_theorem(equivalent(equivalent(X, Y), equivalent(Y, X))) = true.
% 25.02/3.76 Axiom 3 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 25.02/3.78 Axiom 4 (ec_5): is_a_theorem(equivalent(equivalent(equivalent(X, Y), Z), equivalent(X, equivalent(Y, Z)))) = true.
% 25.02/3.78
% 25.02/3.78 Goal 1 (prove_ec_1): is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))) = true.
% 25.02/3.78 Proof:
% 25.02/3.78 is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))
% 25.02/3.78 = { by axiom 1 (ifeq_axiom) R->L }
% 25.02/3.78 ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.78 = { by axiom 3 (condensed_detachment) R->L }
% 25.02/3.78 ifeq(ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.78 = { by axiom 1 (ifeq_axiom) R->L }
% 25.02/3.78 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.78 = { by axiom 3 (condensed_detachment) R->L }
% 25.02/3.78 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.78 = { by axiom 4 (ec_5) }
% 25.02/3.79 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.79 = { by axiom 1 (ifeq_axiom) }
% 25.02/3.79 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.79 = { by axiom 4 (ec_5) }
% 25.02/3.79 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.79 = { by axiom 1 (ifeq_axiom) }
% 25.02/3.79 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.79 = { by axiom 1 (ifeq_axiom) R->L }
% 25.02/3.79 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.79 = { by axiom 2 (ec_4) R->L }
% 25.02/3.80 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c))), true), true), true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.80 = { by axiom 3 (condensed_detachment) }
% 25.02/3.80 ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.80 = { by axiom 1 (ifeq_axiom) }
% 25.02/3.80 ifeq(ifeq(is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.80 = { by axiom 1 (ifeq_axiom) R->L }
% 25.02/3.80 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.02/3.80 = { by axiom 3 (condensed_detachment) R->L }
% 25.02/3.81 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.81 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.81 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.81 = { by axiom 4 (ec_5) R->L }
% 25.72/3.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.81 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.81 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.81 = { by axiom 2 (ec_4) R->L }
% 25.72/3.81 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.82 = { by axiom 3 (condensed_detachment) }
% 25.72/3.82 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.82 = { by axiom 1 (ifeq_axiom) }
% 25.72/3.82 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.82 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.82 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.82 = { by axiom 3 (condensed_detachment) R->L }
% 25.72/3.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.82 = { by axiom 2 (ec_4) }
% 25.72/3.82 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.83 = { by axiom 1 (ifeq_axiom) }
% 25.72/3.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.83 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.83 = { by axiom 3 (condensed_detachment) R->L }
% 25.72/3.83 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.84 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.84 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.85 = { by axiom 4 (ec_5) R->L }
% 25.72/3.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.85 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.85 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.85 = { by axiom 4 (ec_5) R->L }
% 25.72/3.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.86 = { by axiom 3 (condensed_detachment) }
% 25.72/3.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.86 = { by axiom 1 (ifeq_axiom) }
% 25.72/3.86 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.86 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.87 = { by axiom 4 (ec_5) R->L }
% 25.72/3.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.87 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.87 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.87 = { by axiom 4 (ec_5) R->L }
% 25.72/3.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true, is_a_theorem(equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.88 = { by axiom 3 (condensed_detachment) }
% 25.72/3.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.88 = { by axiom 1 (ifeq_axiom) }
% 25.72/3.88 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.89 = { by axiom 1 (ifeq_axiom) R->L }
% 25.72/3.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.89 = { by axiom 3 (condensed_detachment) R->L }
% 25.72/3.89 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.90 = { by axiom 2 (ec_4) }
% 25.72/3.90 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 25.72/3.90 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.91 = { by axiom 1 (ifeq_axiom) R->L }
% 26.44/3.91 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.92 = { by axiom 3 (condensed_detachment) R->L }
% 26.44/3.92 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.93 = { by axiom 4 (ec_5) }
% 26.44/3.93 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.93 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.94 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.94 = { by axiom 4 (ec_5) }
% 26.44/3.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.95 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.95 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.96 = { by axiom 1 (ifeq_axiom) R->L }
% 26.44/3.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.96 = { by axiom 2 (ec_4) R->L }
% 26.44/3.96 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b))), equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(c, a), equivalent(a, b)))), true, is_a_theorem(equivalent(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.97 = { by axiom 3 (condensed_detachment) }
% 26.44/3.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.97 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(equivalent(equivalent(c, a), equivalent(a, b)), equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(a, b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.97 = { by axiom 3 (condensed_detachment) }
% 26.44/3.97 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.97 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.97 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.98 = { by axiom 1 (ifeq_axiom) R->L }
% 26.44/3.98 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.98 = { by axiom 3 (condensed_detachment) R->L }
% 26.44/3.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.98 = { by axiom 2 (ec_4) }
% 26.44/3.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.98 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.98 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 4 (ec_5) }
% 26.44/3.99 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.99 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, equivalent(equivalent(c, a), equivalent(equivalent(a, b), b))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(equivalent(c, a), equivalent(equivalent(a, b), b)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 3 (condensed_detachment) }
% 26.44/3.99 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 1 (ifeq_axiom) }
% 26.44/3.99 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 1 (ifeq_axiom) R->L }
% 26.44/3.99 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/3.99 = { by axiom 3 (condensed_detachment) R->L }
% 26.44/3.99 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/4.00 = { by axiom 1 (ifeq_axiom) R->L }
% 26.44/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 26.44/4.00 = { by axiom 4 (ec_5) R->L }
% 26.44/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.00 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.01 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.01 = { by axiom 2 (ec_4) R->L }
% 27.17/4.01 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.01 = { by axiom 3 (condensed_detachment) }
% 27.17/4.01 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.01 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.01 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.02 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.02 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.02 = { by axiom 3 (condensed_detachment) R->L }
% 27.17/4.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true, ifeq(is_a_theorem(equivalent(equivalent(a, b), equivalent(b, a))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.02 = { by axiom 2 (ec_4) }
% 27.17/4.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.02 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.02 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.02 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.03 = { by axiom 4 (ec_5) R->L }
% 27.17/4.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(a, b), equivalent(b, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.03 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(a, b), equivalent(b, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.03 = { by axiom 2 (ec_4) R->L }
% 27.17/4.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(a, b), equivalent(b, a))), equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(a, b), equivalent(b, a)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(b, a)), equivalent(equivalent(equivalent(a, b), b), a))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.03 = { by axiom 3 (condensed_detachment) }
% 27.17/4.03 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.04 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.04 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.04 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.04 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.04 = { by axiom 3 (condensed_detachment) R->L }
% 27.17/4.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.05 = { by axiom 4 (ec_5) }
% 27.17/4.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.05 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.05 = { by axiom 4 (ec_5) }
% 27.17/4.05 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.05 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.06 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), b), a), equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, b), b), a)), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(equivalent(a, b), b), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.06 = { by axiom 3 (condensed_detachment) }
% 27.17/4.06 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.06 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.06 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b)), equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)), equivalent(equivalent(a, b), b))), true, is_a_theorem(equivalent(a, equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), equivalent(c, a)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.06 = { by axiom 3 (condensed_detachment) }
% 27.17/4.06 ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.06 = { by axiom 1 (ifeq_axiom) }
% 27.17/4.06 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true)
% 27.17/4.06 = { by axiom 1 (ifeq_axiom) R->L }
% 27.17/4.06 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true), true)
% 27.17/4.06 = { by axiom 4 (ec_5) R->L }
% 27.17/4.06 ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c), equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), b), c)), true, is_a_theorem(equivalent(equivalent(equivalent(a, b), equivalent(c, a)), equivalent(b, c))), true), true)
% 27.17/4.06 = { by axiom 3 (condensed_detachment) }
% 27.17/4.06 true
% 27.17/4.06 % SZS output end Proof
% 27.17/4.06
% 27.17/4.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------