Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL384-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:49:43 AM UTC 2026

% Result   : Unsatisfiable 98.82s 13.08s
% Output   : Proof 110.71s
% 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 v2.3.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n020.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Sun Sep 27 15:39:34 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.82/13.08  Command-line arguments: --no-flatten-goal
% 98.82/13.08  
% 98.82/13.08  % SZS status Unsatisfiable
% 98.82/13.08  
% 106.75/13.93  % SZS output start Proof
% 106.75/13.93  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 106.75/13.93  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 106.75/13.93  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 106.75/13.93  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.
% 106.75/13.95  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 106.75/13.95  
% 106.75/13.95  Goal 1 (prove_cn_45): is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))) = true.
% 106.75/13.95  Proof:
% 106.75/13.95    is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z))))
% 106.75/13.95  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/13.95    ifeq(true, true, is_a_theorem(implies(implies(x, implies(y, z)), implies(implies(not(z), y), implies(x, z)))), true)
% 106.75/13.96  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/13.96    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)
% 106.75/13.96  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/13.96    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)
% 106.75/13.96  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/13.96    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)
% 106.75/13.96  = { by axiom 5 (cn_1) }
% 106.75/13.96    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)
% 106.75/13.97  = { by axiom 1 (ifeq_axiom) }
% 106.75/13.97    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)
% 106.75/13.97  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/13.97    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)
% 106.75/13.98  = { by axiom 5 (cn_1) R->L }
% 106.75/13.98    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)
% 106.75/13.98  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/13.98    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)
% 106.75/13.98  = { by axiom 3 (cn_2) R->L }
% 106.75/13.99    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)
% 106.75/13.99  = { by axiom 4 (condensed_detachment) }
% 106.75/13.99    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)
% 106.75/13.99  = { by axiom 1 (ifeq_axiom) }
% 106.75/13.99    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)
% 106.75/13.99  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/13.99    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)
% 106.75/14.00  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/14.00    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)
% 106.75/14.00  = { by axiom 5 (cn_1) }
% 106.75/14.00    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)
% 106.75/14.00  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.01    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)
% 106.75/14.01  = { by axiom 5 (cn_1) }
% 106.75/14.01    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)
% 106.75/14.01  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.01    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)
% 106.75/14.01  = { by axiom 4 (condensed_detachment) }
% 106.75/14.01    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)
% 106.75/14.01  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.01    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)
% 106.75/14.01  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.01    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)
% 106.75/14.02  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/14.02    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)
% 106.75/14.02  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.02    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)
% 106.75/14.02  = { by axiom 5 (cn_1) R->L }
% 106.75/14.02    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)
% 106.75/14.03  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.03    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)
% 106.75/14.03  = { by axiom 5 (cn_1) R->L }
% 106.75/14.03    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)
% 106.75/14.03  = { by axiom 4 (condensed_detachment) }
% 106.75/14.03    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)
% 106.75/14.03  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.03    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)
% 106.75/14.03  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.03    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)
% 106.75/14.04  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/14.04    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)
% 106.75/14.04  = { by axiom 2 (cn_3) }
% 106.75/14.04    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)
% 106.75/14.04  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.04    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)
% 106.75/14.05  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.05    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)
% 106.75/14.05  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/14.05    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)
% 106.75/14.06  = { by axiom 5 (cn_1) }
% 106.75/14.06    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)
% 106.75/14.06  = { by axiom 1 (ifeq_axiom) }
% 106.75/14.07    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)
% 106.75/14.07  = { by axiom 1 (ifeq_axiom) R->L }
% 106.75/14.07    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)
% 106.75/14.07  = { by axiom 4 (condensed_detachment) R->L }
% 106.75/14.08    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)
% 106.75/14.08  = { by axiom 5 (cn_1) }
% 106.75/14.08    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)
% 108.08/14.09  = { by axiom 1 (ifeq_axiom) }
% 108.08/14.09    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)
% 108.08/14.09  = { by axiom 1 (ifeq_axiom) R->L }
% 108.08/14.09    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)
% 108.08/14.10  = { by axiom 3 (cn_2) R->L }
% 108.08/14.10    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)
% 108.08/14.10  = { by axiom 1 (ifeq_axiom) R->L }
% 108.08/14.11    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)
% 108.08/14.11  = { by axiom 2 (cn_3) R->L }
% 108.08/14.11    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)
% 108.08/14.11  = { by axiom 4 (condensed_detachment) }
% 108.08/14.12    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)
% 108.08/14.12  = { by axiom 1 (ifeq_axiom) }
% 108.08/14.13    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)
% 108.08/14.13  = { by axiom 1 (ifeq_axiom) R->L }
% 108.08/14.13    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)
% 108.08/14.14  = { by axiom 4 (condensed_detachment) R->L }
% 108.08/14.14    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)
% 108.08/14.15  = { by axiom 2 (cn_3) }
% 108.08/14.15    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)
% 108.08/14.16  = { by axiom 1 (ifeq_axiom) }
% 108.08/14.16    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)
% 108.08/14.16  = { by axiom 5 (cn_1) }
% 108.08/14.16    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)
% 108.08/14.16  = { by axiom 1 (ifeq_axiom) }
% 108.08/14.17    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)
% 108.08/14.17  = { by axiom 4 (condensed_detachment) }
% 108.08/14.17    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)
% 108.08/14.18  = { by axiom 1 (ifeq_axiom) }
% 108.96/14.18    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)
% 108.96/14.19  = { by axiom 1 (ifeq_axiom) R->L }
% 108.96/14.19    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)
% 108.96/14.20  = { by axiom 4 (condensed_detachment) R->L }
% 108.96/14.21    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)
% 109.12/14.22  = { by axiom 1 (ifeq_axiom) R->L }
% 109.12/14.23    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)
% 109.12/14.24  = { by axiom 5 (cn_1) R->L }
% 109.12/14.25    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)
% 109.12/14.26  = { by axiom 1 (ifeq_axiom) R->L }
% 109.12/14.26    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)
% 109.12/14.27  = { by axiom 5 (cn_1) R->L }
% 109.12/14.28    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)
% 109.12/14.29  = { by axiom 4 (condensed_detachment) }
% 109.12/14.29    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)
% 109.12/14.30  = { by axiom 1 (ifeq_axiom) }
% 109.89/14.30    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)
% 109.89/14.31  = { by axiom 1 (ifeq_axiom) R->L }
% 109.89/14.32    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)
% 109.89/14.32  = { by axiom 4 (condensed_detachment) R->L }
% 109.89/14.33    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)
% 109.89/14.33  = { by axiom 3 (cn_2) }
% 109.89/14.34    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)
% 109.89/14.34  = { by axiom 1 (ifeq_axiom) }
% 109.89/14.35    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)
% 109.89/14.36  = { by axiom 5 (cn_1) }
% 109.89/14.36    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)
% 109.89/14.37  = { by axiom 1 (ifeq_axiom) }
% 109.89/14.37    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)
% 109.89/14.38  = { by axiom 1 (ifeq_axiom) R->L }
% 109.89/14.38    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)
% 109.89/14.39  = { by axiom 5 (cn_1) R->L }
% 109.89/14.39    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)
% 109.89/14.39  = { by axiom 4 (condensed_detachment) }
% 109.89/14.39    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)
% 109.89/14.40  = { by axiom 1 (ifeq_axiom) }
% 109.89/14.40    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)
% 109.89/14.40  = { by axiom 4 (condensed_detachment) }
% 109.89/14.40    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)
% 109.89/14.40  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.40    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)
% 110.71/14.41  = { by axiom 1 (ifeq_axiom) R->L }
% 110.71/14.41    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)
% 110.71/14.41  = { by axiom 4 (condensed_detachment) R->L }
% 110.71/14.41    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)
% 110.71/14.42  = { by axiom 5 (cn_1) }
% 110.71/14.42    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)
% 110.71/14.42  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.42    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)
% 110.71/14.43  = { by axiom 1 (ifeq_axiom) R->L }
% 110.71/14.43    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)
% 110.71/14.43  = { by axiom 5 (cn_1) R->L }
% 110.71/14.43    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)
% 110.71/14.43  = { by axiom 1 (ifeq_axiom) R->L }
% 110.71/14.44    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)
% 110.71/14.44  = { by axiom 3 (cn_2) R->L }
% 110.71/14.44    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)
% 110.71/14.44  = { by axiom 4 (condensed_detachment) }
% 110.71/14.44    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)
% 110.71/14.44  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.45    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)
% 110.71/14.45  = { by axiom 4 (condensed_detachment) }
% 110.71/14.45    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)
% 110.71/14.45  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.45    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)
% 110.71/14.45  = { by axiom 1 (ifeq_axiom) R->L }
% 110.71/14.45    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)
% 110.71/14.45  = { by axiom 4 (condensed_detachment) R->L }
% 110.71/14.45    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)
% 110.71/14.45  = { by axiom 5 (cn_1) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 5 (cn_1) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 4 (condensed_detachment) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) R->L }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 4 (condensed_detachment) R->L }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 5 (cn_1) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 5 (cn_1) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 1 (ifeq_axiom) }
% 110.71/14.46    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)
% 110.71/14.46  = { by axiom 4 (condensed_detachment) }
% 110.71/14.46    true
% 110.71/14.46  % SZS output end Proof
% 110.71/14.46  
% 110.71/14.46  RESULT: Unsatisfiable (the axioms are contradictory).
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