Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL428-1 : TPTP v9.3.1. Bugfixed v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 11:49:50 AM UTC 2026

% Result   : Unsatisfiable 184.50s 23.85s
% Output   : Proof 245.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL428-1 : TPTP v9.3.1. Bugfixed v5.5.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n020.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Sun Sep 27 15:42:49 UTC 2026
% 0.12/0.36  % CPUTime  : 
% 0.12/0.36  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 184.50/23.85  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 184.50/23.85  
% 184.50/23.85  % SZS status Unsatisfiable
% 184.50/23.85  
% 222.64/28.68  % SZS output start Proof
% 222.64/28.68  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 222.64/28.68  Axiom 2 (mv1): is_a_theorem(implies(X, implies(Y, X))) = true.
% 222.64/28.68  Axiom 3 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 222.64/28.68  Axiom 4 (mv2): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 222.64/28.68  Axiom 5 (mv3): is_a_theorem(implies(implies(implies(X, Y), Y), implies(implies(Y, X), X))) = true.
% 223.43/28.77  Axiom 6 (mv5): is_a_theorem(implies(implies(implies(X, Y), implies(Y, X)), implies(Y, X))) = true.
% 223.43/28.77  
% 223.43/28.77  Goal 1 (prove_hr): is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)) = true.
% 223.43/28.77  Proof:
% 223.43/28.77    is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))
% 223.43/28.77  = { by axiom 1 (ifeq_axiom) R->L }
% 223.43/28.77    ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true)
% 223.43/28.77  = { by axiom 1 (ifeq_axiom) R->L }
% 223.43/28.77    ifeq(true, true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 223.43/28.78  = { by axiom 3 (condensed_detachment) R->L }
% 223.43/28.78    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)))), true, ifeq(is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 223.43/28.79  = { by axiom 4 (mv2) }
% 223.43/28.79    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 223.43/28.80  = { by axiom 1 (ifeq_axiom) }
% 223.43/28.80    ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.80  = { by axiom 1 (ifeq_axiom) R->L }
% 224.22/28.81    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.81  = { by axiom 3 (condensed_detachment) R->L }
% 224.22/28.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x))))), true, ifeq(is_a_theorem(implies(x, implies(y, x))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.82  = { by axiom 2 (mv1) }
% 224.22/28.82    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(y, x))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.83  = { by axiom 1 (ifeq_axiom) }
% 224.22/28.83    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(y, x))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.83  = { by axiom 2 (mv1) }
% 224.22/28.84    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.84  = { by axiom 1 (ifeq_axiom) }
% 224.22/28.85    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.85  = { by axiom 1 (ifeq_axiom) R->L }
% 224.22/28.85    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.86  = { by axiom 5 (mv3) R->L }
% 224.22/28.86    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x))), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(x, implies(y, x))), implies(x, implies(y, x)))), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.87  = { by axiom 3 (condensed_detachment) }
% 224.22/28.87    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.88  = { by axiom 1 (ifeq_axiom) }
% 224.22/28.88    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.89  = { by axiom 3 (condensed_detachment) R->L }
% 224.22/28.89    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 224.22/28.90  = { by axiom 1 (ifeq_axiom) R->L }
% 224.22/28.90    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.91  = { by axiom 3 (condensed_detachment) R->L }
% 225.02/28.91    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(v14, implies(v15, v14)), implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14))))), true, ifeq(is_a_theorem(implies(v14, implies(v15, v14))), true, is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true), true), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.92  = { by axiom 2 (mv1) }
% 225.02/28.92    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(v14, implies(v15, v14))), true, is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true), true), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.92  = { by axiom 1 (ifeq_axiom) }
% 225.02/28.93    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(v14, implies(v15, v14))), true, is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.93  = { by axiom 2 (mv1) }
% 225.02/28.94    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.94  = { by axiom 1 (ifeq_axiom) }
% 225.02/28.95    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.95  = { by axiom 1 (ifeq_axiom) R->L }
% 225.02/28.96    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.96  = { by axiom 5 (mv3) R->L }
% 225.02/28.96    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14))), implies(implies(implies(v14, implies(v15, v14)), v16), v16))), true, ifeq(is_a_theorem(implies(implies(v16, implies(v14, implies(v15, v14))), implies(v14, implies(v15, v14)))), true, is_a_theorem(implies(implies(implies(v14, implies(v15, v14)), v16), v16)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.97  = { by axiom 3 (condensed_detachment) }
% 225.02/28.97    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.98  = { by axiom 1 (ifeq_axiom) }
% 225.02/28.98    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/28.99  = { by axiom 1 (ifeq_axiom) R->L }
% 225.02/28.99    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.00  = { by axiom 3 (condensed_detachment) R->L }
% 225.02/29.00    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.01  = { by axiom 5 (mv3) }
% 225.02/29.02    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.02  = { by axiom 1 (ifeq_axiom) }
% 225.02/29.03    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.04  = { by axiom 1 (ifeq_axiom) R->L }
% 225.02/29.05    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.06  = { by axiom 3 (condensed_detachment) R->L }
% 225.02/29.06    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 225.02/29.07  = { by axiom 1 (ifeq_axiom) R->L }
% 226.36/29.08    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 226.36/29.09  = { by axiom 3 (condensed_detachment) R->L }
% 226.36/29.10    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 226.36/29.11  = { by axiom 5 (mv3) }
% 226.36/29.12    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 226.36/29.13  = { by axiom 1 (ifeq_axiom) }
% 226.36/29.14    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 226.36/29.15  = { by axiom 1 (ifeq_axiom) R->L }
% 226.36/29.16    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 226.36/29.18  = { by axiom 3 (condensed_detachment) R->L }
% 227.19/29.19    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 227.19/29.20  = { by axiom 1 (ifeq_axiom) R->L }
% 227.40/29.22    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 227.40/29.23  = { by axiom 3 (condensed_detachment) R->L }
% 227.40/29.24    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 227.40/29.26  = { by axiom 5 (mv3) }
% 227.40/29.27    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 227.40/29.28  = { by axiom 1 (ifeq_axiom) }
% 227.40/29.30    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.15/29.31  = { by axiom 1 (ifeq_axiom) R->L }
% 228.15/29.33    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.15/29.34  = { by axiom 3 (condensed_detachment) R->L }
% 228.15/29.36    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.15/29.38  = { by axiom 1 (ifeq_axiom) R->L }
% 228.15/29.39    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.97/29.41  = { by axiom 3 (condensed_detachment) R->L }
% 228.97/29.43    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.97/29.44  = { by axiom 5 (mv3) }
% 228.97/29.46    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 228.97/29.47  = { by axiom 1 (ifeq_axiom) }
% 228.97/29.49    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 229.76/29.50  = { by axiom 1 (ifeq_axiom) R->L }
% 229.76/29.52    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 229.76/29.54  = { by axiom 3 (condensed_detachment) R->L }
% 229.76/29.56    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 229.76/29.57  = { by axiom 1 (ifeq_axiom) R->L }
% 229.76/29.59    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 230.55/29.61  = { by axiom 2 (mv1) R->L }
% 230.55/29.63    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, u), implies(implies(implies(v, u), implies(z, u)), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 230.55/29.64  = { by axiom 1 (ifeq_axiom) R->L }
% 230.55/29.66    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(z, u), implies(implies(implies(v, u), implies(z, u)), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 230.55/29.67  = { by axiom 4 (mv2) R->L }
% 230.55/29.70    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, u), implies(implies(implies(v, u), implies(z, u)), implies(z, u))), implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u)))))), true, ifeq(is_a_theorem(implies(implies(z, u), implies(implies(implies(v, u), implies(z, u)), implies(z, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 231.36/29.71  = { by axiom 3 (condensed_detachment) }
% 231.36/29.73    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 231.36/29.74  = { by axiom 1 (ifeq_axiom) }
% 231.36/29.76    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 231.36/29.78  = { by axiom 1 (ifeq_axiom) R->L }
% 231.36/29.80    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.15/29.81  = { by axiom 3 (condensed_detachment) R->L }
% 232.15/29.83    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v, z), implies(implies(z, u), implies(v, u))), implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))))), true, ifeq(is_a_theorem(implies(implies(v, z), implies(implies(z, u), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.15/29.85  = { by axiom 4 (mv2) }
% 232.15/29.86    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(v, z), implies(implies(z, u), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.15/29.88  = { by axiom 1 (ifeq_axiom) }
% 232.91/29.90    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(v, z), implies(implies(z, u), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.91/29.92  = { by axiom 4 (mv2) }
% 232.91/29.94    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.91/29.95  = { by axiom 1 (ifeq_axiom) }
% 232.91/29.97    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.91/29.99  = { by axiom 1 (ifeq_axiom) R->L }
% 232.91/30.01    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.91/30.03  = { by axiom 3 (condensed_detachment) R->L }
% 232.91/30.05    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(implies(z, u), implies(v, u)), implies(v, u))), implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(implies(z, u), implies(v, u)), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 232.91/30.07  = { by axiom 4 (mv2) }
% 234.26/30.09    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(implies(z, u), implies(v, u)), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 234.26/30.11  = { by axiom 1 (ifeq_axiom) }
% 234.26/30.13    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(implies(z, u), implies(v, u)), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 234.26/30.14  = { by axiom 5 (mv3) }
% 234.26/30.16    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 234.26/30.17  = { by axiom 1 (ifeq_axiom) }
% 235.10/30.20    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(v, u)), implies(v, u)), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(v, u), implies(z, u)), implies(z, u)), implies(implies(v, z), implies(v, u)))), true), true), true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 235.29/30.21  = { by axiom 3 (condensed_detachment) }
% 235.29/30.23    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 235.29/30.24  = { by axiom 1 (ifeq_axiom) }
% 235.29/30.26    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 235.29/30.27  = { by axiom 1 (ifeq_axiom) R->L }
% 235.29/30.29    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 235.29/30.30  = { by axiom 2 (mv1) R->L }
% 236.08/30.32    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u)))))), true, ifeq(is_a_theorem(implies(implies(z, u), implies(implies(v, z), implies(v, u)))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), implies(implies(z, u), implies(implies(v, z), implies(v, u)))), implies(implies(z, u), implies(implies(v, z), implies(v, u))))), true), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.08/30.33  = { by axiom 3 (condensed_detachment) }
% 236.08/30.35    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.08/30.36  = { by axiom 1 (ifeq_axiom) }
% 236.08/30.38    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.08/30.39  = { by axiom 1 (ifeq_axiom) R->L }
% 236.88/30.41    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.88/30.42  = { by axiom 4 (mv2) R->L }
% 236.88/30.44    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7)), implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), implies(implies(w, implies(v6, w)), v7))), true, is_a_theorem(implies(implies(implies(implies(w, implies(v6, w)), v7), v7), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.88/30.45  = { by axiom 3 (condensed_detachment) }
% 236.88/30.46    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 236.88/30.48  = { by axiom 1 (ifeq_axiom) }
% 236.88/30.49    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 237.67/30.51  = { by axiom 1 (ifeq_axiom) R->L }
% 237.67/30.52    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 237.67/30.53  = { by axiom 3 (condensed_detachment) R->L }
% 237.67/30.55    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(w, implies(v6, w)), implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w))))), true, ifeq(is_a_theorem(implies(w, implies(v6, w))), true, is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true), true), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 237.67/30.57  = { by axiom 2 (mv1) }
% 237.67/30.59    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(w, implies(v6, w))), true, is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true), true), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 237.67/30.60  = { by axiom 1 (ifeq_axiom) }
% 238.53/30.61    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(w, implies(v6, w))), true, is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 238.53/30.63  = { by axiom 2 (mv1) }
% 238.53/30.64    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 238.53/30.65  = { by axiom 1 (ifeq_axiom) }
% 238.53/30.67    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 238.53/30.68  = { by axiom 1 (ifeq_axiom) R->L }
% 238.53/30.70    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 239.26/30.71  = { by axiom 5 (mv3) R->L }
% 239.26/30.73    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w))), implies(implies(implies(w, implies(v6, w)), v7), v7))), true, ifeq(is_a_theorem(implies(implies(v7, implies(w, implies(v6, w))), implies(w, implies(v6, w)))), true, is_a_theorem(implies(implies(implies(w, implies(v6, w)), v7), v7)), true), true), true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 239.26/30.74  = { by axiom 3 (condensed_detachment) }
% 239.26/30.75    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 239.26/30.77  = { by axiom 1 (ifeq_axiom) }
% 239.26/30.78    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 239.26/30.79  = { by axiom 1 (ifeq_axiom) R->L }
% 240.07/30.81    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.07/30.81  = { by axiom 2 (mv1) R->L }
% 240.07/30.83    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7)), implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.07/30.84  = { by axiom 3 (condensed_detachment) }
% 240.07/30.86    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.07/30.87  = { by axiom 1 (ifeq_axiom) }
% 240.07/30.88    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.07/30.89  = { by axiom 1 (ifeq_axiom) R->L }
% 240.85/30.90    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/30.91  = { by axiom 4 (mv2) R->L }
% 240.85/30.93    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/30.94  = { by axiom 3 (condensed_detachment) }
% 240.85/30.95    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/30.96  = { by axiom 1 (ifeq_axiom) }
% 240.85/30.97    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/30.98  = { by axiom 1 (ifeq_axiom) R->L }
% 240.85/30.99    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/31.00  = { by axiom 3 (condensed_detachment) R->L }
% 240.85/31.01    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))))), true, ifeq(is_a_theorem(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), true, is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/31.02  = { by axiom 2 (mv1) }
% 240.85/31.03    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), true, is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/31.04  = { by axiom 1 (ifeq_axiom) }
% 240.85/31.05    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), true, is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 240.85/31.06  = { by axiom 5 (mv3) }
% 240.85/31.07    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 242.22/31.08  = { by axiom 1 (ifeq_axiom) }
% 242.22/31.10    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 242.22/31.11  = { by axiom 1 (ifeq_axiom) R->L }
% 242.22/31.12    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 242.22/31.13  = { by axiom 5 (mv3) R->L }
% 242.22/31.14    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10))), true, ifeq(is_a_theorem(implies(implies(v10, implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8))), implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)))), true, is_a_theorem(implies(implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10), v10)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 242.22/31.15  = { by axiom 3 (condensed_detachment) }
% 242.22/31.16    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 242.22/31.17  = { by axiom 1 (ifeq_axiom) }
% 242.22/31.18    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.05/31.19  = { by axiom 1 (ifeq_axiom) R->L }
% 243.05/31.20    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.05/31.21  = { by axiom 2 (mv1) R->L }
% 243.26/31.22    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10)), implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.23  = { by axiom 3 (condensed_detachment) }
% 243.26/31.24    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.24  = { by axiom 1 (ifeq_axiom) }
% 243.26/31.25    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.26  = { by axiom 1 (ifeq_axiom) R->L }
% 243.26/31.27    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.27  = { by axiom 4 (mv2) R->L }
% 243.26/31.28    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.29  = { by axiom 3 (condensed_detachment) }
% 243.26/31.30    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.26/31.30  = { by axiom 1 (ifeq_axiom) }
% 243.26/31.31    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.32  = { by axiom 1 (ifeq_axiom) R->L }
% 243.96/31.32    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.33  = { by axiom 3 (condensed_detachment) R->L }
% 243.96/31.34    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))))), true, ifeq(is_a_theorem(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), true, is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.34  = { by axiom 2 (mv1) }
% 243.96/31.35    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), true, is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.36  = { by axiom 1 (ifeq_axiom) }
% 243.96/31.37    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), true, is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.37  = { by axiom 6 (mv5) }
% 243.96/31.38    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.39  = { by axiom 1 (ifeq_axiom) }
% 243.96/31.39    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 243.96/31.40  = { by axiom 1 (ifeq_axiom) R->L }
% 244.57/31.41    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.41  = { by axiom 5 (mv3) R->L }
% 244.57/31.42    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13))), true, ifeq(is_a_theorem(implies(implies(v13, implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11))), implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)))), true, is_a_theorem(implies(implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13), v13)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.43  = { by axiom 3 (condensed_detachment) }
% 244.57/31.43    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.44  = { by axiom 1 (ifeq_axiom) }
% 244.57/31.45    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.46  = { by axiom 1 (ifeq_axiom) R->L }
% 244.57/31.46    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.47  = { by axiom 2 (mv1) R->L }
% 244.57/31.48    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13)), implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.48  = { by axiom 3 (condensed_detachment) }
% 244.57/31.48    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.49  = { by axiom 1 (ifeq_axiom) }
% 244.57/31.49    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.50  = { by axiom 1 (ifeq_axiom) R->L }
% 244.57/31.50    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 244.57/31.50  = { by axiom 4 (mv2) R->L }
% 245.30/31.51    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), implies(implies(v14, implies(v15, v14)), v16))), true, is_a_theorem(implies(implies(implies(implies(v14, implies(v15, v14)), v16), v16), implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 245.30/31.51  = { by axiom 3 (condensed_detachment) }
% 245.30/31.51    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 245.30/31.51  = { by axiom 1 (ifeq_axiom) }
% 245.30/31.52    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16), implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16)), v16)), true, is_a_theorem(implies(implies(implies(x, implies(y, x)), implies(implies(implies(implies(implies(implies(implies(implies(implies(z, u), implies(implies(v, z), implies(v, u))), implies(implies(w, implies(v6, w)), v7)), v7), implies(implies(implies(implies(v8, v9), v9), implies(implies(v9, v8), v8)), v10)), v10), implies(implies(implies(implies(v11, v12), implies(v12, v11)), implies(v12, v11)), v13)), v13), implies(implies(v14, implies(v15, v14)), v16))), v16)), true), true)
% 245.30/31.52  = { by axiom 3 (condensed_detachment) }
% 245.30/31.52    true
% 245.30/31.52  % SZS output end Proof
% 245.30/31.52  
% 245.30/31.52  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------