%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:06 AM UTC 2026
% Result : Unsatisfiable 20.31s 2.93s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL128-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 15:22:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.31/2.93 Command-line arguments: --no-flatten-goal
% 20.31/2.93
% 20.31/2.93 % SZS status Unsatisfiable
% 20.31/2.93
% 223.18/28.48 % SZS output start Proof
% 223.18/28.48 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 223.18/28.48 Axiom 2 (condensed_detachment): ifeq(is_a_theorem(equivalent(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 225.56/28.78 Axiom 3 (s_3): is_a_theorem(equivalent(X, equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(W, Z)), equivalent(Y, W))))) = true.
% 225.56/28.78
% 225.56/28.79 Goal 1 (prove_lg_2): is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))) = true.
% 225.56/28.79 Proof:
% 225.56/28.79 is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))
% 225.56/28.79 = { by axiom 1 (ifeq_axiom) R->L }
% 225.56/28.79 ifeq(true, true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 225.56/28.79 = { by axiom 2 (condensed_detachment) R->L }
% 225.56/28.79 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 225.56/28.79 = { by axiom 1 (ifeq_axiom) R->L }
% 225.56/28.79 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 225.56/28.79 = { by axiom 2 (condensed_detachment) R->L }
% 225.56/28.79 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 225.56/28.80 = { by axiom 3 (s_3) }
% 226.37/28.80 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 226.37/28.80 = { by axiom 1 (ifeq_axiom) }
% 226.37/28.80 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 226.37/28.81 = { by axiom 1 (ifeq_axiom) R->L }
% 226.37/28.81 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 226.37/28.81 = { by axiom 2 (condensed_detachment) R->L }
% 226.37/28.81 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), 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% 226.37/28.82 = { by axiom 3 (s_3) }
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% 226.37/28.82 = { by axiom 1 (ifeq_axiom) }
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% 226.37/28.83 = { by axiom 1 (ifeq_axiom) R->L }
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% 226.37/28.84 = { by axiom 3 (s_3) R->L }
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% 226.37/28.84 = { by axiom 1 (ifeq_axiom) R->L }
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% 226.37/28.85 = { by axiom 2 (condensed_detachment) R->L }
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% 226.37/28.85 = { by axiom 3 (s_3) }
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% 226.37/28.86 = { by axiom 1 (ifeq_axiom) }
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% 226.37/28.87 = { by axiom 3 (s_3) }
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% 226.37/28.87 = { by axiom 1 (ifeq_axiom) }
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% 226.37/28.88 = { by axiom 2 (condensed_detachment) }
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% 226.37/28.89 = { by axiom 1 (ifeq_axiom) }
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% 226.37/28.89 = { by axiom 1 (ifeq_axiom) R->L }
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% 227.14/28.92 = { by axiom 3 (s_3) R->L }
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% 227.14/28.94 = { by axiom 1 (ifeq_axiom) R->L }
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% 227.14/28.94 = { by axiom 3 (s_3) R->L }
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% 227.14/28.96 = { by axiom 2 (condensed_detachment) }
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% 227.14/28.97 = { by axiom 3 (s_3) }
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% 227.14/28.97 = { by axiom 1 (ifeq_axiom) }
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% 227.14/28.98 = { by axiom 2 (condensed_detachment) }
% 227.14/28.98 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/28.98 = { by axiom 1 (ifeq_axiom) }
% 227.14/28.98 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/28.98 = { by axiom 1 (ifeq_axiom) R->L }
% 227.14/28.99 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/28.99 = { by axiom 2 (condensed_detachment) R->L }
% 227.14/28.99 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/28.99 = { by axiom 1 (ifeq_axiom) R->L }
% 227.14/28.99 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.00 = { by axiom 3 (s_3) R->L }
% 227.14/29.00 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.00 = { by axiom 1 (ifeq_axiom) R->L }
% 227.14/29.00 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.00 = { by axiom 2 (condensed_detachment) R->L }
% 227.14/29.00 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))))), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.00 = { by axiom 3 (s_3) }
% 227.14/29.01 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.01 = { by axiom 1 (ifeq_axiom) }
% 227.14/29.01 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.01 = { by axiom 3 (s_3) }
% 227.14/29.01 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.02 = { by axiom 1 (ifeq_axiom) }
% 227.14/29.02 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))))), true, ifeq(is_a_theorem(equivalent(Y2, equivalent(Y2, equivalent(equivalent(equivalent(Z2, W2), equivalent(V2, W2)), equivalent(Z2, V2))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.02 = { by axiom 2 (condensed_detachment) }
% 227.14/29.02 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.02 = { by axiom 1 (ifeq_axiom) }
% 227.14/29.02 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.03 = { by axiom 1 (ifeq_axiom) R->L }
% 227.14/29.03 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 227.14/29.03 = { by axiom 2 (condensed_detachment) R->L }
% 227.14/29.03 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.03 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.04 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.04 = { by axiom 3 (s_3) R->L }
% 228.17/29.04 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.04 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.05 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.05 = { by axiom 2 (condensed_detachment) R->L }
% 228.17/29.05 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))))), true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))))), true), true), true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), 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true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.05 = { by axiom 3 (s_3) }
% 228.17/29.06 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), 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equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.06 = { by axiom 1 (ifeq_axiom) }
% 228.17/29.06 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))))), true), true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.06 = { by axiom 3 (s_3) }
% 228.17/29.07 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))))), true), true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.07 = { by axiom 1 (ifeq_axiom) }
% 228.17/29.07 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3)))), equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))))), true, ifeq(is_a_theorem(equivalent(T2, equivalent(T2, equivalent(equivalent(equivalent(S2, X3), equivalent(Y3, X3)), equivalent(S2, Y3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.07 = { by axiom 2 (condensed_detachment) }
% 228.17/29.08 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.08 = { by axiom 1 (ifeq_axiom) }
% 228.17/29.08 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.08 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.08 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.09 = { by axiom 2 (condensed_detachment) R->L }
% 228.17/29.09 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.09 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.09 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.09 = { by axiom 3 (s_3) R->L }
% 228.17/29.10 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.10 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.10 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.10 = { by axiom 3 (s_3) R->L }
% 228.17/29.11 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))))), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true), true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.11 = { by axiom 2 (condensed_detachment) }
% 228.17/29.11 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.11 = { by axiom 1 (ifeq_axiom) }
% 228.17/29.11 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(Z3, equivalent(Z3, equivalent(equivalent(equivalent(W3, V3), equivalent(U3, V3)), equivalent(W3, U3))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.12 = { by axiom 3 (s_3) }
% 228.17/29.12 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.12 = { by axiom 1 (ifeq_axiom) }
% 228.17/29.12 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.12 = { by axiom 1 (ifeq_axiom) R->L }
% 228.17/29.13 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.17/29.13 = { by axiom 3 (s_3) R->L }
% 228.93/29.13 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), U2)))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.13 = { by axiom 2 (condensed_detachment) }
% 228.93/29.13 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.14 = { by axiom 1 (ifeq_axiom) }
% 228.93/29.14 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.14 = { by axiom 1 (ifeq_axiom) R->L }
% 228.93/29.14 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.14 = { by axiom 2 (condensed_detachment) R->L }
% 228.93/29.14 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))))), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.15 = { by axiom 1 (ifeq_axiom) R->L }
% 228.93/29.15 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))))), true), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.15 = { by axiom 3 (s_3) R->L }
% 228.93/29.15 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))))), true), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.16 = { by axiom 1 (ifeq_axiom) R->L }
% 228.93/29.16 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))))), true), true), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.16 = { by axiom 3 (s_3) R->L }
% 228.93/29.16 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))))), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4)))), equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))))), true), true), true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.17 = { by axiom 2 (condensed_detachment) }
% 228.93/29.17 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.17 = { by axiom 1 (ifeq_axiom) }
% 228.93/29.17 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(T3, equivalent(T3, equivalent(equivalent(equivalent(S3, X4), equivalent(Y4, X4)), equivalent(S3, Y4))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.17 = { by axiom 3 (s_3) }
% 228.93/29.17 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.18 = { by axiom 1 (ifeq_axiom) }
% 228.93/29.18 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2)))), true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(U2, X2)))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), X2))), true), true), true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.18 = { by axiom 2 (condensed_detachment) }
% 228.93/29.18 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.18 = { by axiom 1 (ifeq_axiom) }
% 228.93/29.18 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(is_a_theorem(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.18 = { by axiom 2 (condensed_detachment) }
% 228.93/29.18 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.18 = { by axiom 1 (ifeq_axiom) }
% 228.93/29.18 ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 228.93/29.19 = { by axiom 1 (ifeq_axiom) R->L }
% 228.93/29.19 ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 229.49/29.21 = { by axiom 2 (condensed_detachment) R->L }
% 229.49/29.21 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 229.49/29.22 = { by axiom 1 (ifeq_axiom) R->L }
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% 244.04/31.12 = { by axiom 2 (condensed_detachment) }
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% 244.85/31.14 = { by axiom 1 (ifeq_axiom) }
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% 244.85/31.16 = { by axiom 1 (ifeq_axiom) R->L }
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% 244.85/31.18 = { by axiom 2 (condensed_detachment) R->L }
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% 245.34/31.21 = { by axiom 1 (ifeq_axiom) R->L }
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% 245.34/31.25 = { by axiom 3 (s_3) R->L }
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% 245.34/31.29 = { by axiom 1 (ifeq_axiom) R->L }
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% 246.13/31.32 = { by axiom 2 (condensed_detachment) R->L }
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% 246.13/31.36 = { by axiom 3 (s_3) }
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% 246.94/31.40 = { by axiom 1 (ifeq_axiom) }
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% 247.73/31.57 = { by axiom 1 (ifeq_axiom) R->L }
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% 248.54/31.60 = { by axiom 2 (condensed_detachment) R->L }
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% 251.92/32.12 = { by axiom 2 (condensed_detachment) }
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% 252.71/32.16 = { by axiom 1 (ifeq_axiom) }
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% 253.34/32.20 = { by axiom 1 (ifeq_axiom) R->L }
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% 253.34/32.24 = { by axiom 2 (condensed_detachment) R->L }
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% 253.34/32.29 = { by axiom 1 (ifeq_axiom) R->L }
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% 254.09/32.33 = { by axiom 3 (s_3) R->L }
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% 254.09/32.37 = { by axiom 1 (ifeq_axiom) R->L }
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% 257.31/32.71 = { by axiom 1 (ifeq_axiom) }
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% 257.31/32.75 = { by axiom 1 (ifeq_axiom) R->L }
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% 257.31/32.78 = { by axiom 2 (condensed_detachment) R->L }
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% 258.12/32.82 = { by axiom 1 (ifeq_axiom) R->L }
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% 258.89/32.90 = { by axiom 1 (ifeq_axiom) R->L }
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% 258.89/32.99 = { by axiom 2 (condensed_detachment) }
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% 258.89/33.02 = { by axiom 1 (ifeq_axiom) }
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% 259.99/33.05 = { by axiom 3 (s_3) }
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% 259.99/33.07 = { by axiom 1 (ifeq_axiom) }
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% 259.99/33.09 = { by axiom 2 (condensed_detachment) }
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% 259.99/33.10 = { by axiom 1 (ifeq_axiom) }
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% 259.99/33.11 = { by axiom 2 (condensed_detachment) }
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% 259.99/33.13 = { by axiom 1 (ifeq_axiom) }
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% 260.80/33.15 = { by axiom 1 (ifeq_axiom) R->L }
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% 260.80/33.18 = { by axiom 2 (condensed_detachment) R->L }
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% 261.28/33.22 = { by axiom 1 (ifeq_axiom) R->L }
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% 261.28/33.28 = { by axiom 3 (s_3) R->L }
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% 264.47/33.69 = { by axiom 1 (ifeq_axiom) R->L }
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% 266.06/33.81 = { by axiom 1 (ifeq_axiom) R->L }
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% 266.06/33.84 = { by axiom 3 (s_3) R->L }
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% 266.06/33.87 = { by axiom 2 (condensed_detachment) }
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% 266.06/33.89 = { by axiom 1 (ifeq_axiom) }
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% 266.82/33.92 = { by axiom 3 (s_3) }
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% 266.82/33.94 = { by axiom 1 (ifeq_axiom) }
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% 266.82/33.95 = { by axiom 1 (ifeq_axiom) R->L }
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% 266.82/33.97 = { by axiom 3 (s_3) R->L }
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% 266.82/33.99 = { by axiom 2 (condensed_detachment) }
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% 266.82/34.00 = { by axiom 1 (ifeq_axiom) }
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% 266.82/34.00 = { by axiom 1 (ifeq_axiom) R->L }
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% 266.82/34.00 = { by axiom 3 (s_3) R->L }
% 266.82/34.01 ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c)))), equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), 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% 266.82/34.02 = { by axiom 2 (condensed_detachment) }
% 266.82/34.02 ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 267.63/34.02 = { by axiom 1 (ifeq_axiom) }
% 267.63/34.02 ifeq(ifeq(ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 267.63/34.03 = { by axiom 1 (ifeq_axiom) R->L }
% 267.63/34.03 ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))), true), true), true, is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 267.63/34.03 = { by axiom 2 (condensed_detachment) R->L }
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% 267.63/34.05 = { by axiom 1 (ifeq_axiom) R->L }
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% 267.63/34.06 = { by axiom 3 (s_3) R->L }
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% 267.63/34.08 = { by axiom 1 (ifeq_axiom) R->L }
% 267.63/34.09 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(equivalent(V8, equivalent(V8, equivalent(equivalent(equivalent(U8, T8), equivalent(S8, T8)), equivalent(U8, S8))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(b, c))), equivalent(equivalent(a, equivalent(equivalent(b, c), 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% 267.63/34.10 = { by axiom 2 (condensed_detachment) R->L }
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% 268.33/34.14 = { by axiom 1 (ifeq_axiom) }
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% 268.33/34.18 = { by axiom 3 (s_3) }
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% 268.33/34.19 = { by axiom 1 (ifeq_axiom) }
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% 268.90/34.21 = { by axiom 2 (condensed_detachment) }
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% 268.90/34.22 = { by axiom 1 (ifeq_axiom) }
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% 268.90/34.23 = { by axiom 1 (ifeq_axiom) R->L }
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% 268.90/34.24 = { by axiom 2 (condensed_detachment) R->L }
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% 268.90/34.26 = { by axiom 1 (ifeq_axiom) R->L }
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% 268.90/34.28 = { by axiom 3 (s_3) R->L }
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% 270.30/34.41 = { by axiom 2 (condensed_detachment) }
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% 270.30/34.43 = { by axiom 1 (ifeq_axiom) }
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% 270.30/34.44 = { by axiom 1 (ifeq_axiom) R->L }
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% 270.30/34.46 = { by axiom 2 (condensed_detachment) R->L }
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% 271.01/34.53 = { by axiom 3 (s_3) R->L }
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% 271.01/34.56 = { by axiom 1 (ifeq_axiom) R->L }
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% 271.01/34.58 = { by axiom 2 (condensed_detachment) R->L }
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% 273.81/35.01 = { by axiom 2 (condensed_detachment) }
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% 274.64/35.02 = { by axiom 1 (ifeq_axiom) }
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% 274.64/35.04 = { by axiom 1 (ifeq_axiom) R->L }
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% 275.94/35.27 = { by axiom 1 (ifeq_axiom) R->L }
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% 275.94/35.27 = { by axiom 3 (s_3) R->L }
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% 275.94/35.28 = { by axiom 2 (condensed_detachment) }
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% 275.94/35.29 = { by axiom 1 (ifeq_axiom) }
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% 275.94/35.29 = { by axiom 2 (condensed_detachment) }
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% 275.94/35.29 = { by axiom 1 (ifeq_axiom) }
% 275.94/35.29 ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true)
% 275.94/35.29 = { by axiom 1 (ifeq_axiom) R->L }
% 275.94/35.29 ifeq(true, true, ifeq(is_a_theorem(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true, is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))))), true), true)
% 275.94/35.30 = { by axiom 2 (condensed_detachment) R->L }
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% 276.64/35.30 = { by axiom 1 (ifeq_axiom) R->L }
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% 276.64/35.31 = { by axiom 2 (condensed_detachment) R->L }
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% 276.64/35.32 = { by axiom 3 (s_3) }
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% 276.64/35.32 = { by axiom 1 (ifeq_axiom) }
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% 276.64/35.33 = { by axiom 1 (ifeq_axiom) R->L }
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% 276.64/35.34 = { by axiom 3 (s_3) R->L }
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% 276.64/35.35 = { by axiom 1 (ifeq_axiom) R->L }
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% 276.64/35.36 = { by axiom 2 (condensed_detachment) R->L }
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% 276.64/35.36 = { by axiom 3 (s_3) }
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% 276.64/35.37 = { by axiom 1 (ifeq_axiom) }
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% 276.64/35.37 = { by axiom 3 (s_3) }
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% 276.64/35.37 = { by axiom 1 (ifeq_axiom) }
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% 276.64/35.38 = { by axiom 2 (condensed_detachment) }
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% 276.64/35.38 = { by axiom 1 (ifeq_axiom) }
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% 276.64/35.39 = { by axiom 1 (ifeq_axiom) R->L }
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% 276.64/35.39 = { by axiom 2 (condensed_detachment) R->L }
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% 277.34/35.40 = { by axiom 1 (ifeq_axiom) R->L }
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% 277.34/35.43 = { by axiom 3 (s_3) R->L }
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% 277.34/35.44 = { by axiom 2 (condensed_detachment) }
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% 277.34/35.44 = { by axiom 1 (ifeq_axiom) }
% 277.34/35.45 ifeq(ifeq(ifeq(ifeq(is_a_theorem(equivalent(T11, equivalent(T11, equivalent(equivalent(equivalent(S11, X12), equivalent(Y12, X12)), equivalent(S11, Y12))))), true, is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))), equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(a, equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), equivalent(c, e))))), equivalent(equivalent(equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e)))), equivalent(equivalent(equivalent(equivalent(b, e), equivalent(c, e)), equivalent(equivalent(b, e), 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% 277.34/35.45 = { by axiom 3 (s_3) }
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% 277.34/35.45 = { by axiom 1 (ifeq_axiom) }
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% 277.34/35.45 = { by axiom 2 (condensed_detachment) }
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% 277.34/35.46 = { by axiom 1 (ifeq_axiom) }
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% 277.34/35.46 = { by axiom 1 (ifeq_axiom) R->L }
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% 277.34/35.47 = { by axiom 2 (condensed_detachment) R->L }
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% 277.34/35.47 = { by axiom 1 (ifeq_axiom) R->L }
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% 277.34/35.48 = { by axiom 2 (condensed_detachment) R->L }
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% 278.04/35.50 = { by axiom 1 (ifeq_axiom) }
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% 278.04/35.51 = { by axiom 1 (ifeq_axiom) R->L }
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% 278.04/35.55 = { by axiom 2 (condensed_detachment) R->L }
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% 278.04/35.56 = { by axiom 3 (s_3) }
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% 278.04/35.57 = { by axiom 1 (ifeq_axiom) }
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% 278.73/35.64 = { by axiom 1 (ifeq_axiom) R->L }
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% 280.22/35.81 = { by axiom 2 (condensed_detachment) }
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% 280.22/35.81 = { by axiom 1 (ifeq_axiom) }
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% 280.22/35.82 = { by axiom 1 (ifeq_axiom) R->L }
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% 280.22/35.84 = { by axiom 2 (condensed_detachment) R->L }
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% 280.22/35.90 = { by axiom 1 (ifeq_axiom) R->L }
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% 299.85/38.66 = { by axiom 3 (s_3) R->L }
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