Twee---2.7.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n011.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 11:49:43 AM UTC 2026

% Result   : Theorem 78.04s 10.31s
% Output   : Proof 85.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL384+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n011.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 27 15:38:30 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.04/10.31  Command-line arguments: --no-flatten-goal
% 78.04/10.31  
% 78.04/10.31  % SZS status Theorem
% 78.04/10.31  
% 82.02/10.86  % SZS output start Proof
% 82.02/10.86  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 82.02/10.86  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 82.02/10.86  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 82.02/10.86  Axiom 4 (condensed_detachment): ifeq(is_a_theorem(implies(X, Y)), true, ifeq(is_a_theorem(X), true, is_a_theorem(Y), true), true) = true.
% 82.02/10.87  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 82.02/10.87  
% 82.02/10.87  Goal 1 (prove_cn_45): is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))) = true.
% 82.02/10.87  Proof:
% 82.02/10.87    is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))
% 82.02/10.88  = { by axiom 1 (ifeq_axiom) R->L }
% 82.02/10.88    ifeq(true, true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 4 (condensed_detachment) R->L }
% 82.02/10.88    ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 1 (ifeq_axiom) R->L }
% 82.02/10.88    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 4 (condensed_detachment) R->L }
% 82.02/10.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z))), implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 5 (cn_1) }
% 82.02/10.88    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 1 (ifeq_axiom) }
% 82.02/10.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 1 (ifeq_axiom) R->L }
% 82.02/10.88    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 5 (cn_1) R->L }
% 82.02/10.88    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z))))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.88  = { by axiom 1 (ifeq_axiom) R->L }
% 82.02/10.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.89  = { by axiom 3 (cn_2) R->L }
% 82.02/10.89    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.89  = { by axiom 4 (condensed_detachment) }
% 82.02/10.89    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.89  = { by axiom 1 (ifeq_axiom) }
% 82.02/10.90    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.90  = { by axiom 1 (ifeq_axiom) R->L }
% 82.02/10.90    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.02/10.90  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/10.90    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 5 (cn_1) }
% 82.81/10.91    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.91    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 5 (cn_1) }
% 82.81/10.91    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true, is_a_theorem(implies(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 4 (condensed_detachment) }
% 82.81/10.91    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.91  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.92    ifeq(ifeq(is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.92    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/10.92    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.92    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 5 (cn_1) R->L }
% 82.81/10.92    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.92    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.92  = { by axiom 5 (cn_1) R->L }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z))), implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(implies(implies(not(z), z), z), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 4 (condensed_detachment) }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 2 (cn_3) }
% 82.81/10.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.93  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.94  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.94  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/10.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.95  = { by axiom 5 (cn_1) }
% 82.81/10.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.95  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.95  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.96  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/10.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z)))), implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.97  = { by axiom 5 (cn_1) }
% 82.81/10.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.97  = { by axiom 1 (ifeq_axiom) }
% 82.81/10.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.98  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.98  = { by axiom 3 (cn_2) R->L }
% 82.81/10.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.99  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/10.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/10.99  = { by axiom 2 (cn_3) R->L }
% 82.81/11.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), z), z), implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), z), z)), true, is_a_theorem(implies(not(implies(implies(not(z), z), z)), not(not(implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.00  = { by axiom 4 (condensed_detachment) }
% 82.81/11.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.01  = { by axiom 1 (ifeq_axiom) }
% 82.81/11.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.03  = { by axiom 1 (ifeq_axiom) R->L }
% 82.81/11.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.04  = { by axiom 4 (condensed_detachment) R->L }
% 82.81/11.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.06  = { by axiom 2 (cn_3) }
% 82.81/11.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.07  = { by axiom 1 (ifeq_axiom) }
% 82.81/11.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z))), implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.08  = { by axiom 5 (cn_1) }
% 82.81/11.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.08  = { by axiom 1 (ifeq_axiom) }
% 82.81/11.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(y, z), z))), implies(implies(not(z), z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true, is_a_theorem(implies(not(implies(implies(y, z), z)), implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 82.81/11.09  = { by axiom 4 (condensed_detachment) }
% 82.81/11.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.10  = { by axiom 1 (ifeq_axiom) }
% 84.27/11.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.11  = { by axiom 1 (ifeq_axiom) R->L }
% 84.27/11.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.12  = { by axiom 4 (condensed_detachment) R->L }
% 84.27/11.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.14  = { by axiom 1 (ifeq_axiom) R->L }
% 84.27/11.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.16  = { by axiom 5 (cn_1) R->L }
% 84.27/11.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.17  = { by axiom 1 (ifeq_axiom) R->L }
% 84.27/11.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.18  = { by axiom 5 (cn_1) R->L }
% 84.27/11.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 84.27/11.19  = { by axiom 4 (condensed_detachment) }
% 85.09/11.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.09/11.20  = { by axiom 1 (ifeq_axiom) }
% 85.09/11.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.21  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.21    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.21  = { by axiom 4 (condensed_detachment) R->L }
% 85.18/11.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.22  = { by axiom 3 (cn_2) }
% 85.18/11.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.22  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(y, z), z)), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.23  = { by axiom 5 (cn_1) }
% 85.18/11.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.23  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.24  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.24  = { by axiom 5 (cn_1) R->L }
% 85.18/11.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.25  = { by axiom 4 (condensed_detachment) }
% 85.18/11.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.25  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.25  = { by axiom 4 (condensed_detachment) }
% 85.18/11.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.26  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.26    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.26  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.26    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.26  = { by axiom 4 (condensed_detachment) R->L }
% 85.18/11.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.26  = { by axiom 5 (cn_1) }
% 85.18/11.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.26  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.27  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.27  = { by axiom 5 (cn_1) R->L }
% 85.18/11.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.27  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 3 (cn_2) R->L }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(not(z), z), z))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 4 (condensed_detachment) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(z), z), z)), implies(implies(not(z), z), z)), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(implies(implies(not(z), z), z), implies(implies(y, z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 4 (condensed_detachment) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.28    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.28    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 4 (condensed_detachment) R->L }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z))), implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))))), true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 5 (cn_1) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(z), y), implies(implies(y, z), implies(not(z), z)))), true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 5 (cn_1) }
% 85.18/11.28    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.28    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))), implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z))))), true, ifeq(is_a_theorem(implies(implies(implies(y, z), implies(not(z), z)), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true, is_a_theorem(implies(implies(not(z), y), implies(not(implies(implies(y, z), z)), implies(implies(y, z), z)))), true), true), true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.28  = { by axiom 4 (condensed_detachment) }
% 85.18/11.29    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.29  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.29    ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 85.18/11.29  = { by axiom 1 (ifeq_axiom) R->L }
% 85.18/11.29    ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 4 (condensed_detachment) R->L }
% 85.18/11.29    ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), z), implies(x, z))), implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))))), true, ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), z), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 5 (cn_1) }
% 85.18/11.29    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), z), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.29    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(implies(y, z), z), implies(x, z)))), true, is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 5 (cn_1) }
% 85.18/11.29    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 1 (ifeq_axiom) }
% 85.18/11.29    ifeq(is_a_theorem(implies(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z))), implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(y, z), z), implies(x, z)), implies(implies(not(z), y), implies(x, z)))), true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true), true)
% 85.18/11.29  = { by axiom 4 (condensed_detachment) }
% 85.18/11.29    true
% 85.18/11.29  % SZS output end Proof
% 85.18/11.29  
% 85.18/11.29  RESULT: Theorem (the conjecture is true).
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