Twee---2.7.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL400-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n026.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 11:49:46 AM UTC 2026

% Result   : Unsatisfiable 81.88s 10.96s
% Output   : Proof 144.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : LCL400-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44  % Computer : n026.cluster.edu
% 0.17/0.44  % Model    : x86_64 x86_64
% 0.17/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44  % Memory   : 8046.5625MB
% 0.17/0.44  % OS       : Linux 6.8.0-71-generic
% 0.17/0.44  % CPULimit : 300
% 0.17/0.44  % WCLimit  : 300
% 0.17/0.44  % DateTime : Sun Sep 27 15:42:56 UTC 2026
% 0.17/0.44  % CPUTime  : 
% 0.17/0.44  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.88/10.96  Command-line arguments: --no-flatten-goal
% 81.88/10.96  
% 81.88/10.96  % SZS status Unsatisfiable
% 81.88/10.96  
% 112.50/16.79  % SZS output start Proof
% 112.50/16.79  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 112.50/16.79  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 112.50/16.79  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 112.50/16.79  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.
% 114.14/16.99  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 114.14/16.99  
% 114.14/16.99  Goal 1 (prove_cn_66): is_a_theorem(implies(not(implies(x, y)), x)) = true.
% 114.14/16.99  Proof:
% 114.14/16.99    is_a_theorem(implies(not(implies(x, y)), x))
% 114.14/16.99  = { by axiom 1 (ifeq_axiom) R->L }
% 114.14/16.99    ifeq(true, true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.14/16.99  = { by axiom 4 (condensed_detachment) R->L }
% 114.14/16.99    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.14/16.99  = { by axiom 1 (ifeq_axiom) R->L }
% 114.14/16.99    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.14/17.00  = { by axiom 4 (condensed_detachment) R->L }
% 114.14/17.00    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.14/17.00  = { by axiom 5 (cn_1) }
% 114.62/17.00    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.00  = { by axiom 1 (ifeq_axiom) }
% 114.62/17.00    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.00  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.00    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.01  = { by axiom 4 (condensed_detachment) R->L }
% 114.62/17.01    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.01  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.02    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.02  = { by axiom 5 (cn_1) R->L }
% 114.62/17.02    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.02  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.03    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.03  = { by axiom 5 (cn_1) R->L }
% 114.62/17.03    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.04  = { by axiom 4 (condensed_detachment) }
% 114.62/17.04    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.04  = { by axiom 1 (ifeq_axiom) }
% 114.62/17.04    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.04  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.05    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.05  = { by axiom 4 (condensed_detachment) R->L }
% 114.62/17.05    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.06  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.06    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.06  = { by axiom 4 (condensed_detachment) R->L }
% 114.62/17.07    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.07  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.07    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.08  = { by axiom 5 (cn_1) R->L }
% 114.62/17.08    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), x)), implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.09  = { by axiom 1 (ifeq_axiom) R->L }
% 114.62/17.09    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), x)), implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 114.62/17.09  = { by axiom 2 (cn_3) R->L }
% 114.62/17.10    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(not(implies(x, y))), x)), implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(is_a_theorem(implies(not(implies(x, y)), implies(not(not(implies(x, y))), x))), true, is_a_theorem(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.10  = { by axiom 4 (condensed_detachment) }
% 115.33/17.10    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.11  = { by axiom 1 (ifeq_axiom) }
% 115.33/17.11    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.11  = { by axiom 1 (ifeq_axiom) R->L }
% 115.33/17.12    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.12  = { by axiom 4 (condensed_detachment) R->L }
% 115.33/17.13    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))))), true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.13  = { by axiom 1 (ifeq_axiom) R->L }
% 115.33/17.14    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.14  = { by axiom 5 (cn_1) R->L }
% 115.33/17.15    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(not(implies(x, y))))), implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))))), true, is_a_theorem(implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.15  = { by axiom 1 (ifeq_axiom) R->L }
% 115.33/17.16    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(not(implies(x, y))))), implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.16  = { by axiom 2 (cn_3) R->L }
% 115.33/17.17    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), not(not(implies(x, y))))), implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))))), true, ifeq(is_a_theorem(implies(x, implies(not(x), not(not(implies(x, y)))))), true, is_a_theorem(implies(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.17  = { by axiom 4 (condensed_detachment) }
% 115.33/17.17    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.18  = { by axiom 1 (ifeq_axiom) }
% 115.33/17.18    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(x), not(not(implies(x, y)))), implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.18  = { by axiom 5 (cn_1) }
% 115.33/17.19    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.19  = { by axiom 1 (ifeq_axiom) }
% 115.33/17.19    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 115.33/17.20  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.20    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.20  = { by axiom 5 (cn_1) R->L }
% 116.04/17.21    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x))), implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x)))))), true, ifeq(is_a_theorem(implies(x, implies(implies(not(not(implies(x, y))), x), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(x, y))), x), implies(not(x), x)), implies(not(implies(x, y)), implies(not(x), x))), implies(x, implies(not(implies(x, y)), implies(not(x), x))))), true), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.21  = { by axiom 4 (condensed_detachment) }
% 116.04/17.21    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.22  = { by axiom 1 (ifeq_axiom) }
% 116.04/17.22    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.22  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.22    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.22  = { by axiom 5 (cn_1) R->L }
% 116.04/17.23    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), implies(not(x), x))), implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(x, implies(not(implies(x, y)), implies(not(x), x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.23  = { by axiom 4 (condensed_detachment) }
% 116.04/17.23    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.24  = { by axiom 1 (ifeq_axiom) }
% 116.04/17.24    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.24  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.24    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.25  = { by axiom 4 (condensed_detachment) R->L }
% 116.04/17.25    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, x), implies(implies(not(x), x), x)), implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.25  = { by axiom 5 (cn_1) }
% 116.04/17.25    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.26  = { by axiom 1 (ifeq_axiom) }
% 116.04/17.26    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.26  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.26    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.27  = { by axiom 5 (cn_1) R->L }
% 116.04/17.27    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.27  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.27    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, ifeq(true, true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.28  = { by axiom 3 (cn_2) R->L }
% 116.04/17.28    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(implies(x, x), implies(implies(not(x), x), x)))), true, ifeq(is_a_theorem(implies(implies(not(x), x), x)), true, is_a_theorem(implies(implies(x, x), implies(implies(not(x), x), x))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.29  = { by axiom 4 (condensed_detachment) }
% 116.04/17.29    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.29  = { by axiom 1 (ifeq_axiom) }
% 116.04/17.29    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.04/17.29  = { by axiom 1 (ifeq_axiom) R->L }
% 116.04/17.30    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.30  = { by axiom 4 (condensed_detachment) R->L }
% 116.75/17.30    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x))), implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.31  = { by axiom 5 (cn_1) }
% 116.75/17.31    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.31  = { by axiom 1 (ifeq_axiom) }
% 116.75/17.32    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.32  = { by axiom 5 (cn_1) }
% 116.75/17.32    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.32  = { by axiom 1 (ifeq_axiom) }
% 116.75/17.33    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(x), x), x), implies(not(implies(x, y)), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(x, y)), implies(not(x), x)), implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.33  = { by axiom 4 (condensed_detachment) }
% 116.75/17.33    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.33  = { by axiom 1 (ifeq_axiom) }
% 116.75/17.33    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.33  = { by axiom 1 (ifeq_axiom) R->L }
% 116.75/17.34    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.34  = { by axiom 5 (cn_1) R->L }
% 116.75/17.34    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x))), implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(x, implies(implies(x, x), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(x, x), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.34  = { by axiom 4 (condensed_detachment) }
% 116.75/17.34    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.35  = { by axiom 1 (ifeq_axiom) }
% 116.75/17.35    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.35  = { by axiom 1 (ifeq_axiom) R->L }
% 116.75/17.35    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.35  = { by axiom 4 (condensed_detachment) R->L }
% 116.75/17.35    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.36  = { by axiom 3 (cn_2) }
% 116.75/17.36    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.36  = { by axiom 1 (ifeq_axiom) }
% 116.75/17.36    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.37  = { by axiom 1 (ifeq_axiom) R->L }
% 116.75/17.37    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.37  = { by axiom 4 (condensed_detachment) R->L }
% 116.75/17.37    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.38  = { by axiom 1 (ifeq_axiom) R->L }
% 116.75/17.38    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.38  = { by axiom 5 (cn_1) R->L }
% 116.75/17.39    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), implies(x, x))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.39  = { by axiom 1 (ifeq_axiom) R->L }
% 116.75/17.39    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), implies(x, x))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 116.75/17.40  = { by axiom 2 (cn_3) R->L }
% 117.47/17.42    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), implies(x, x))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.42  = { by axiom 4 (condensed_detachment) }
% 117.47/17.42    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.42  = { by axiom 1 (ifeq_axiom) }
% 117.47/17.42    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.43  = { by axiom 1 (ifeq_axiom) R->L }
% 117.47/17.43    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.43  = { by axiom 4 (condensed_detachment) R->L }
% 117.47/17.43    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, x), implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.44  = { by axiom 2 (cn_3) }
% 117.47/17.44    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.44  = { by axiom 1 (ifeq_axiom) }
% 117.47/17.44    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(x, x)), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.45  = { by axiom 1 (ifeq_axiom) R->L }
% 117.47/17.45    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.45  = { by axiom 4 (condensed_detachment) R->L }
% 117.47/17.46    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, ifeq(is_a_theorem(implies(x, implies(not(x), x))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.46  = { by axiom 2 (cn_3) }
% 117.47/17.46    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.46  = { by axiom 1 (ifeq_axiom) }
% 117.47/17.47    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(x), x)), implies(implies(implies(not(x), x), x), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.47  = { by axiom 5 (cn_1) }
% 117.47/17.47    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.47  = { by axiom 1 (ifeq_axiom) }
% 117.47/17.48    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, is_a_theorem(implies(x, x)), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.48  = { by axiom 1 (ifeq_axiom) R->L }
% 117.47/17.48    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, ifeq(true, true, is_a_theorem(implies(x, x)), true), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.48  = { by axiom 3 (cn_2) R->L }
% 117.47/17.48    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(x), x), x), implies(x, x))), true, ifeq(is_a_theorem(implies(implies(not(x), x), x)), true, is_a_theorem(implies(x, x)), true), true), true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.49  = { by axiom 4 (condensed_detachment) }
% 117.47/17.49    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.49  = { by axiom 1 (ifeq_axiom) }
% 117.47/17.49    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 117.47/17.49  = { by axiom 1 (ifeq_axiom) R->L }
% 117.47/17.50    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.50  = { by axiom 5 (cn_1) R->L }
% 118.17/17.50    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x)))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x))))), true, ifeq(is_a_theorem(implies(not(implies(x, x)), not(not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(x, x)), implies(not(implies(x, x)), implies(x, x)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.50  = { by axiom 4 (condensed_detachment) }
% 118.17/17.51    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.51  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.51    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.51  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.51    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.51  = { by axiom 5 (cn_1) R->L }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x))), implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, x)), implies(x, x)))), true, is_a_theorem(implies(implies(implies(not(implies(x, x)), implies(x, x)), implies(x, x)), implies(not(implies(not(implies(x, y)), x)), implies(x, x)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 4 (condensed_detachment) }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, x)), implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, x))), true, is_a_theorem(implies(x, implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 4 (condensed_detachment) }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true, ifeq(true, true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.52  = { by axiom 3 (cn_2) R->L }
% 118.17/17.52    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(x, implies(not(implies(x, y)), x)))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(x, implies(not(implies(x, y)), x))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.53  = { by axiom 4 (condensed_detachment) }
% 118.17/17.53    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.53  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.53    ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.53  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.53    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.53  = { by axiom 4 (condensed_detachment) R->L }
% 118.17/17.53    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.54  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.54    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.54  = { by axiom 4 (condensed_detachment) R->L }
% 118.17/17.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.55  = { by axiom 5 (cn_1) }
% 118.17/17.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.55  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.56  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.57  = { by axiom 5 (cn_1) R->L }
% 118.17/17.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.57  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.58  = { by axiom 2 (cn_3) R->L }
% 118.17/17.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.58  = { by axiom 4 (condensed_detachment) }
% 118.17/17.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.59  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.59  = { by axiom 1 (ifeq_axiom) R->L }
% 118.17/17.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.59  = { by axiom 5 (cn_1) R->L }
% 118.17/17.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)), implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.59  = { by axiom 4 (condensed_detachment) }
% 118.17/17.59    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.17/17.60  = { by axiom 1 (ifeq_axiom) }
% 118.17/17.60    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.60  = { by axiom 1 (ifeq_axiom) R->L }
% 118.89/17.60    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.61  = { by axiom 4 (condensed_detachment) R->L }
% 118.89/17.61    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.62  = { by axiom 1 (ifeq_axiom) R->L }
% 118.89/17.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.63  = { by axiom 4 (condensed_detachment) R->L }
% 118.89/17.63    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.64  = { by axiom 1 (ifeq_axiom) R->L }
% 118.89/17.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.65  = { by axiom 5 (cn_1) R->L }
% 118.89/17.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.66  = { by axiom 1 (ifeq_axiom) R->L }
% 118.89/17.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.68  = { by axiom 2 (cn_3) R->L }
% 118.89/17.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.69  = { by axiom 4 (condensed_detachment) }
% 118.89/17.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 118.89/17.70  = { by axiom 1 (ifeq_axiom) }
% 119.59/17.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.71  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.72  = { by axiom 5 (cn_1) R->L }
% 119.59/17.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.72  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.73  = { by axiom 3 (cn_2) R->L }
% 119.59/17.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.74  = { by axiom 4 (condensed_detachment) }
% 119.59/17.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.75  = { by axiom 1 (ifeq_axiom) }
% 119.59/17.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.75  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.76  = { by axiom 5 (cn_1) R->L }
% 119.59/17.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.76  = { by axiom 4 (condensed_detachment) }
% 119.59/17.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.76  = { by axiom 1 (ifeq_axiom) }
% 119.59/17.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.77  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.78  = { by axiom 4 (condensed_detachment) R->L }
% 119.59/17.78    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.79  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.80  = { by axiom 4 (condensed_detachment) R->L }
% 119.59/17.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.81  = { by axiom 5 (cn_1) }
% 119.59/17.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.83  = { by axiom 1 (ifeq_axiom) }
% 119.59/17.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 119.59/17.85  = { by axiom 1 (ifeq_axiom) R->L }
% 119.59/17.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 120.64/17.87  = { by axiom 5 (cn_1) R->L }
% 120.64/17.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 120.64/17.89  = { by axiom 1 (ifeq_axiom) R->L }
% 120.64/17.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 120.64/17.91  = { by axiom 3 (cn_2) R->L }
% 120.64/17.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 120.64/17.94  = { by axiom 4 (condensed_detachment) }
% 120.64/17.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 121.40/17.97  = { by axiom 1 (ifeq_axiom) }
% 121.40/17.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 121.69/18.00  = { by axiom 1 (ifeq_axiom) R->L }
% 121.69/18.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 121.69/18.03  = { by axiom 4 (condensed_detachment) R->L }
% 121.69/18.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 121.69/18.06  = { by axiom 5 (cn_1) }
% 121.69/18.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 121.69/18.09  = { by axiom 1 (ifeq_axiom) }
% 122.38/18.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.11  = { by axiom 5 (cn_1) }
% 122.38/18.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.13  = { by axiom 1 (ifeq_axiom) }
% 122.38/18.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.15  = { by axiom 4 (condensed_detachment) }
% 122.38/18.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.16  = { by axiom 1 (ifeq_axiom) }
% 122.38/18.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.17  = { by axiom 1 (ifeq_axiom) R->L }
% 122.38/18.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.18  = { by axiom 4 (condensed_detachment) R->L }
% 122.38/18.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 122.38/18.20  = { by axiom 5 (cn_1) }
% 123.08/18.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.08/18.21  = { by axiom 1 (ifeq_axiom) }
% 123.08/18.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.08/18.23  = { by axiom 1 (ifeq_axiom) R->L }
% 123.08/18.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.08/18.26  = { by axiom 4 (condensed_detachment) R->L }
% 123.08/18.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.08/18.28  = { by axiom 1 (ifeq_axiom) R->L }
% 123.08/18.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.80/18.31  = { by axiom 5 (cn_1) R->L }
% 123.80/18.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.80/18.33  = { by axiom 1 (ifeq_axiom) R->L }
% 123.80/18.34    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.80/18.35  = { by axiom 5 (cn_1) R->L }
% 123.80/18.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 123.80/18.38  = { by axiom 4 (condensed_detachment) }
% 123.80/18.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 124.50/18.40  = { by axiom 1 (ifeq_axiom) }
% 124.50/18.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 124.50/18.42  = { by axiom 1 (ifeq_axiom) R->L }
% 124.50/18.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 124.50/18.46  = { by axiom 4 (condensed_detachment) R->L }
% 124.50/18.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 124.50/18.49  = { by axiom 1 (ifeq_axiom) R->L }
% 125.20/18.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.20/18.52  = { by axiom 5 (cn_1) R->L }
% 125.20/18.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.20/18.55  = { by axiom 1 (ifeq_axiom) R->L }
% 125.20/18.56    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.20/18.57  = { by axiom 2 (cn_3) R->L }
% 125.20/18.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.90/18.61  = { by axiom 4 (condensed_detachment) }
% 125.90/18.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.90/18.64  = { by axiom 1 (ifeq_axiom) }
% 125.90/18.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.90/18.67  = { by axiom 1 (ifeq_axiom) R->L }
% 125.90/18.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 125.90/18.69  = { by axiom 5 (cn_1) R->L }
% 126.61/18.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.71  = { by axiom 1 (ifeq_axiom) R->L }
% 126.61/18.72    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.74  = { by axiom 3 (cn_2) R->L }
% 126.61/18.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(implies(x, y)), x))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.76  = { by axiom 4 (condensed_detachment) }
% 126.61/18.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.78  = { by axiom 1 (ifeq_axiom) }
% 126.61/18.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.80  = { by axiom 1 (ifeq_axiom) R->L }
% 126.61/18.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 126.61/18.82  = { by axiom 5 (cn_1) R->L }
% 126.61/18.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 127.56/18.84  = { by axiom 4 (condensed_detachment) }
% 127.56/18.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 127.56/18.86  = { by axiom 1 (ifeq_axiom) }
% 127.56/18.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 127.56/18.88  = { by axiom 1 (ifeq_axiom) R->L }
% 127.56/18.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 127.56/18.90  = { by axiom 4 (condensed_detachment) R->L }
% 127.56/18.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 127.56/18.92  = { by axiom 5 (cn_1) }
% 128.27/18.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 128.27/18.96  = { by axiom 1 (ifeq_axiom) }
% 128.27/18.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 128.27/18.99  = { by axiom 1 (ifeq_axiom) R->L }
% 128.27/19.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 128.71/19.02  = { by axiom 4 (condensed_detachment) R->L }
% 128.71/19.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 128.71/19.05  = { by axiom 5 (cn_1) }
% 128.71/19.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 128.71/19.08  = { by axiom 1 (ifeq_axiom) }
% 128.71/19.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 129.42/19.12  = { by axiom 1 (ifeq_axiom) R->L }
% 129.42/19.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 129.42/19.17  = { by axiom 5 (cn_1) R->L }
% 129.42/19.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 130.12/19.22  = { by axiom 1 (ifeq_axiom) R->L }
% 130.12/19.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 130.12/19.26  = { by axiom 4 (condensed_detachment) R->L }
% 130.12/19.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 130.82/19.31  = { by axiom 2 (cn_3) }
% 130.82/19.33    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 130.82/19.35  = { by axiom 1 (ifeq_axiom) }
% 130.82/19.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 130.82/19.39  = { by axiom 5 (cn_1) }
% 131.52/19.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 131.52/19.44  = { by axiom 1 (ifeq_axiom) }
% 131.52/19.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(is_a_theorem(implies(implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 131.52/19.47  = { by axiom 4 (condensed_detachment) }
% 131.52/19.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 132.22/19.52  = { by axiom 1 (ifeq_axiom) }
% 132.22/19.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 132.22/19.57  = { by axiom 1 (ifeq_axiom) R->L }
% 132.22/19.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(true, true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 132.93/19.60  = { by axiom 4 (condensed_detachment) R->L }
% 132.93/19.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(is_a_theorem(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 132.93/19.65  = { by axiom 2 (cn_3) }
% 132.93/19.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 132.93/19.68  = { by axiom 1 (ifeq_axiom) }
% 132.93/19.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.70  = { by axiom 5 (cn_1) }
% 133.64/19.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.72  = { by axiom 1 (ifeq_axiom) }
% 133.64/19.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(not(implies(not(implies(x, y)), x)))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.74  = { by axiom 4 (condensed_detachment) }
% 133.64/19.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.76  = { by axiom 1 (ifeq_axiom) }
% 133.64/19.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), implies(not(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.77  = { by axiom 4 (condensed_detachment) }
% 133.64/19.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.78  = { by axiom 1 (ifeq_axiom) }
% 133.64/19.79    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.80  = { by axiom 1 (ifeq_axiom) R->L }
% 133.64/19.80    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.81  = { by axiom 4 (condensed_detachment) R->L }
% 133.64/19.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 133.64/19.83  = { by axiom 5 (cn_1) }
% 134.59/19.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 134.59/19.85  = { by axiom 1 (ifeq_axiom) }
% 134.59/19.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 134.59/19.88  = { by axiom 1 (ifeq_axiom) R->L }
% 134.59/19.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 134.59/19.90  = { by axiom 5 (cn_1) R->L }
% 134.59/19.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 134.59/19.92  = { by axiom 1 (ifeq_axiom) R->L }
% 134.59/19.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 134.59/19.93  = { by axiom 3 (cn_2) R->L }
% 135.31/19.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.95  = { by axiom 4 (condensed_detachment) }
% 135.31/19.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.96  = { by axiom 1 (ifeq_axiom) }
% 135.31/19.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.97  = { by axiom 4 (condensed_detachment) }
% 135.31/19.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.98  = { by axiom 1 (ifeq_axiom) }
% 135.31/19.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.99  = { by axiom 1 (ifeq_axiom) R->L }
% 135.31/19.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.31/19.99  = { by axiom 4 (condensed_detachment) R->L }
% 135.31/20.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.01  = { by axiom 3 (cn_2) }
% 135.74/20.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.02  = { by axiom 1 (ifeq_axiom) }
% 135.74/20.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.03  = { by axiom 1 (ifeq_axiom) R->L }
% 135.74/20.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.05  = { by axiom 5 (cn_1) R->L }
% 135.74/20.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.06  = { by axiom 1 (ifeq_axiom) R->L }
% 135.74/20.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.06  = { by axiom 2 (cn_3) R->L }
% 135.74/20.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.07  = { by axiom 4 (condensed_detachment) }
% 135.74/20.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.08  = { by axiom 1 (ifeq_axiom) }
% 135.74/20.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.08  = { by axiom 4 (condensed_detachment) }
% 135.74/20.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.09  = { by axiom 1 (ifeq_axiom) }
% 135.74/20.09    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 135.74/20.09  = { by axiom 1 (ifeq_axiom) R->L }
% 135.74/20.09    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.10  = { by axiom 4 (condensed_detachment) R->L }
% 136.44/20.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.11  = { by axiom 1 (ifeq_axiom) R->L }
% 136.44/20.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.12  = { by axiom 5 (cn_1) R->L }
% 136.44/20.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.13  = { by axiom 1 (ifeq_axiom) R->L }
% 136.44/20.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.14  = { by axiom 2 (cn_3) R->L }
% 136.44/20.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y)), implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y))), true, is_a_theorem(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.15  = { by axiom 4 (condensed_detachment) }
% 136.44/20.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.15  = { by axiom 1 (ifeq_axiom) }
% 136.44/20.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.16  = { by axiom 1 (ifeq_axiom) R->L }
% 136.44/20.16    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.17  = { by axiom 5 (cn_1) R->L }
% 136.44/20.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.17  = { by axiom 1 (ifeq_axiom) R->L }
% 136.44/20.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.17  = { by axiom 5 (cn_1) R->L }
% 136.44/20.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))), y), implies(implies(not(implies(x, y)), x), y)), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.18  = { by axiom 4 (condensed_detachment) }
% 136.44/20.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.18  = { by axiom 1 (ifeq_axiom) }
% 136.44/20.18    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y)))), true, ifeq(is_a_theorem(implies(implies(not(implies(x, y)), x), not(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(x, y)), x))), not(implies(not(implies(x, y)), x))), implies(implies(not(implies(x, y)), x), y))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.18  = { by axiom 4 (condensed_detachment) }
% 136.44/20.18    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 1 (ifeq_axiom) }
% 136.44/20.19    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 1 (ifeq_axiom) R->L }
% 136.44/20.19    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 4 (condensed_detachment) R->L }
% 136.44/20.19    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, implies(not(implies(x, y)), x)), implies(implies(implies(not(implies(x, y)), x), y), implies(x, y))), implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))))), true, ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 5 (cn_1) }
% 136.44/20.19    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 1 (ifeq_axiom) }
% 136.44/20.19    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 5 (cn_1) }
% 136.44/20.19    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.19  = { by axiom 1 (ifeq_axiom) }
% 136.44/20.20    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))), implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(x, y)), x), y), implies(x, y)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true, is_a_theorem(implies(implies(x, implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(x, y)))), true), true), true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 136.44/20.20  = { by axiom 4 (condensed_detachment) }
% 136.44/20.20    ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 137.14/20.20  = { by axiom 1 (ifeq_axiom) }
% 137.14/20.20    ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true)
% 137.14/20.20  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.20    ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.20  = { by axiom 4 (condensed_detachment) R->L }
% 137.14/20.20    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.20  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.20    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.20  = { by axiom 5 (cn_1) R->L }
% 137.14/20.20    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.20  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.21    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.21  = { by axiom 5 (cn_1) R->L }
% 137.14/20.21    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.21  = { by axiom 4 (condensed_detachment) }
% 137.14/20.21    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.21  = { by axiom 1 (ifeq_axiom) }
% 137.14/20.21    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.22  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.22    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.22  = { by axiom 4 (condensed_detachment) R->L }
% 137.14/20.23    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.23  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.23    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.24  = { by axiom 4 (condensed_detachment) R->L }
% 137.14/20.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.25  = { by axiom 5 (cn_1) }
% 137.14/20.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.26  = { by axiom 1 (ifeq_axiom) }
% 137.14/20.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.27  = { by axiom 1 (ifeq_axiom) R->L }
% 137.14/20.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.28  = { by axiom 5 (cn_1) R->L }
% 137.14/20.29    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.14/20.29  = { by axiom 1 (ifeq_axiom) R->L }
% 137.84/20.30    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.30  = { by axiom 3 (cn_2) R->L }
% 137.84/20.31    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.32  = { by axiom 4 (condensed_detachment) }
% 137.84/20.32    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.33  = { by axiom 1 (ifeq_axiom) }
% 137.84/20.33    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.34  = { by axiom 1 (ifeq_axiom) R->L }
% 137.84/20.35    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.35  = { by axiom 4 (condensed_detachment) R->L }
% 137.84/20.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.38  = { by axiom 5 (cn_1) }
% 137.84/20.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 137.84/20.40  = { by axiom 1 (ifeq_axiom) }
% 138.55/20.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.40  = { by axiom 5 (cn_1) }
% 138.55/20.41    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.41  = { by axiom 1 (ifeq_axiom) }
% 138.55/20.42    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.42  = { by axiom 4 (condensed_detachment) }
% 138.55/20.42    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.43  = { by axiom 1 (ifeq_axiom) }
% 138.55/20.43    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.43  = { by axiom 1 (ifeq_axiom) R->L }
% 138.55/20.43    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.44  = { by axiom 4 (condensed_detachment) R->L }
% 138.55/20.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.45  = { by axiom 2 (cn_3) }
% 138.55/20.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.45  = { by axiom 1 (ifeq_axiom) }
% 138.55/20.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.46  = { by axiom 1 (ifeq_axiom) R->L }
% 138.55/20.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.47  = { by axiom 4 (condensed_detachment) R->L }
% 138.55/20.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.48  = { by axiom 5 (cn_1) }
% 138.55/20.49    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 138.55/20.49  = { by axiom 1 (ifeq_axiom) }
% 138.55/20.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.50  = { by axiom 1 (ifeq_axiom) R->L }
% 139.25/20.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.51  = { by axiom 4 (condensed_detachment) R->L }
% 139.25/20.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.52  = { by axiom 5 (cn_1) }
% 139.25/20.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.54  = { by axiom 1 (ifeq_axiom) }
% 139.25/20.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.55  = { by axiom 1 (ifeq_axiom) R->L }
% 139.25/20.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.56  = { by axiom 2 (cn_3) R->L }
% 139.25/20.57    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.57  = { by axiom 1 (ifeq_axiom) R->L }
% 139.25/20.58    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.58  = { by axiom 2 (cn_3) R->L }
% 139.25/20.59    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(x, y), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.25/20.60  = { by axiom 4 (condensed_detachment) }
% 139.95/20.60    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.61  = { by axiom 1 (ifeq_axiom) }
% 139.95/20.62    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.63  = { by axiom 1 (ifeq_axiom) R->L }
% 139.95/20.64    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.65  = { by axiom 4 (condensed_detachment) R->L }
% 139.95/20.65    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.66  = { by axiom 2 (cn_3) }
% 139.95/20.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.67  = { by axiom 1 (ifeq_axiom) }
% 139.95/20.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.68  = { by axiom 5 (cn_1) }
% 139.95/20.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.68  = { by axiom 1 (ifeq_axiom) }
% 139.95/20.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 139.95/20.69  = { by axiom 4 (condensed_detachment) }
% 139.95/20.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 140.67/20.70  = { by axiom 1 (ifeq_axiom) }
% 140.67/20.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 140.67/20.72  = { by axiom 1 (ifeq_axiom) R->L }
% 140.67/20.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 140.67/20.75  = { by axiom 4 (condensed_detachment) R->L }
% 140.67/20.77    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 140.67/20.79  = { by axiom 1 (ifeq_axiom) R->L }
% 140.67/20.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), 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implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 140.67/20.84  = { by axiom 5 (cn_1) R->L }
% 141.62/20.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), 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implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), 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implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), 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% 141.62/20.87  = { by axiom 1 (ifeq_axiom) R->L }
% 141.62/20.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), 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x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 141.62/20.90  = { by axiom 5 (cn_1) R->L }
% 141.62/20.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.33/20.94  = { by axiom 4 (condensed_detachment) }
% 142.33/20.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.33/20.96  = { by axiom 1 (ifeq_axiom) }
% 142.33/20.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.33/20.99  = { by axiom 1 (ifeq_axiom) R->L }
% 142.77/21.00    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.77/21.01  = { by axiom 4 (condensed_detachment) R->L }
% 142.77/21.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.77/21.05  = { by axiom 3 (cn_2) }
% 142.77/21.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 142.77/21.07  = { by axiom 1 (ifeq_axiom) }
% 142.77/21.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.10  = { by axiom 5 (cn_1) }
% 143.47/21.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.12  = { by axiom 1 (ifeq_axiom) }
% 143.47/21.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.14  = { by axiom 1 (ifeq_axiom) R->L }
% 143.47/21.15    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.16  = { by axiom 5 (cn_1) R->L }
% 143.47/21.17    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.17  = { by axiom 4 (condensed_detachment) }
% 143.47/21.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.18  = { by axiom 1 (ifeq_axiom) }
% 143.47/21.19    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 143.47/21.19  = { by axiom 4 (condensed_detachment) }
% 143.47/21.20    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.20  = { by axiom 1 (ifeq_axiom) }
% 144.18/21.20    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.21  = { by axiom 1 (ifeq_axiom) R->L }
% 144.18/21.21    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.21  = { by axiom 4 (condensed_detachment) R->L }
% 144.18/21.22    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.22  = { by axiom 5 (cn_1) }
% 144.18/21.23    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.23  = { by axiom 1 (ifeq_axiom) }
% 144.18/21.24    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.25  = { by axiom 1 (ifeq_axiom) R->L }
% 144.18/21.25    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.26  = { by axiom 5 (cn_1) R->L }
% 144.18/21.26    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.26  = { by axiom 1 (ifeq_axiom) R->L }
% 144.18/21.27    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.27  = { by axiom 3 (cn_2) R->L }
% 144.18/21.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.28  = { by axiom 4 (condensed_detachment) }
% 144.18/21.28    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.28  = { by axiom 1 (ifeq_axiom) }
% 144.18/21.29    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(x, y), implies(not(implies(x, y)), x))), implies(implies(x, y), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 4 (condensed_detachment) }
% 144.18/21.29    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 1 (ifeq_axiom) }
% 144.18/21.29    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 1 (ifeq_axiom) R->L }
% 144.18/21.29    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 3 (cn_2) R->L }
% 144.18/21.29    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x)))), true, ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), true, is_a_theorem(implies(implies(implies(implies(x, y), implies(not(implies(x, y)), x)), implies(not(implies(not(implies(x, y)), x)), implies(not(implies(x, y)), x))), implies(not(implies(x, y)), x))), true), true), true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 4 (condensed_detachment) }
% 144.18/21.29    ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 1 (ifeq_axiom) }
% 144.18/21.29    ifeq(is_a_theorem(implies(implies(not(implies(not(implies(x, y)), x)), implies(x, y)), implies(not(implies(x, y)), x))), true, ifeq(is_a_theorem(implies(not(implies(not(implies(x, y)), x)), implies(x, y))), true, is_a_theorem(implies(not(implies(x, y)), x)), true), true)
% 144.18/21.29  = { by axiom 4 (condensed_detachment) }
% 144.18/21.29    true
% 144.18/21.29  % SZS output end Proof
% 144.18/21.29  
% 144.18/21.29  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------