Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL071-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n018.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 11:48:57 AM UTC 2026

% Result   : Unsatisfiable 95.91s 12.55s
% Output   : Proof 99.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL071-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n018.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Sun Sep 27 15:22:53 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.08/0.35  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 95.91/12.55  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 95.91/12.55  
% 95.91/12.55  % SZS status Unsatisfiable
% 95.91/12.55  
% 97.50/12.78  % SZS output start Proof
% 97.50/12.78  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 97.50/12.78  Axiom 2 (cn_19): is_a_theorem(implies(implies(implies(X, Y), Z), implies(Y, Z))) = true.
% 97.50/12.78  Axiom 3 (cn_37): is_a_theorem(implies(implies(implies(X, Y), Z), implies(not(X), Z))) = true.
% 97.50/12.78  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.
% 97.50/12.79  Axiom 5 (cn_60): is_a_theorem(implies(implies(X, implies(not(Y), Z)), implies(X, implies(implies(W, Z), implies(implies(Y, W), Z))))) = true.
% 97.50/12.79  
% 97.50/12.79  Goal 1 (prove_cn_2): is_a_theorem(implies(implies(not(a), a), a)) = true.
% 97.50/12.79  Proof:
% 97.50/12.79    is_a_theorem(implies(implies(not(a), a), a))
% 97.50/12.79  = { by axiom 1 (ifeq_axiom) R->L }
% 97.50/12.79    ifeq(true, true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.79  = { by axiom 4 (condensed_detachment) R->L }
% 97.50/12.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true, ifeq(is_a_theorem(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a))), true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.79  = { by axiom 2 (cn_19) }
% 97.50/12.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true, ifeq(true, true, is_a_theorem(implies(a, a)), true), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.79  = { by axiom 1 (ifeq_axiom) }
% 97.50/12.79    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 4 (condensed_detachment) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 2 (cn_19) }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 1 (ifeq_axiom) }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 5 (cn_60) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(not(implies(implies(X, implies(Y, a)), a)), implies(a, a))), implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(not(implies(implies(X, implies(Y, a)), a)), implies(a, a))), implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 97.50/12.80  = { by axiom 3 (cn_37) R->L }
% 97.50/12.80    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(not(implies(implies(X, implies(Y, a)), a)), implies(a, a))), implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(not(implies(implies(X, implies(Y, a)), a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(implies(X, implies(Y, a)), a), a), implies(a, a)), implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 4 (condensed_detachment) }
% 98.29/12.80    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 2 (cn_19) R->L }
% 98.29/12.80    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y, a), a), implies(a, a)), implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a)))), true, ifeq(is_a_theorem(implies(implies(implies(Y, a), a), implies(a, a))), true, is_a_theorem(implies(implies(implies(implies(X, implies(Y, a)), a), implies(implies(Y, a), a)), implies(a, a))), true), true), true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 4 (condensed_detachment) }
% 98.29/12.80    ifeq(ifeq(true, true, is_a_theorem(implies(a, a)), true), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.80    ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true)
% 98.29/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.80    ifeq(true, true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.80  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.80    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.80  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.80    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.80  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))))), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 5 (cn_60) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))))), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 5 (cn_60) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), implies(not(not(a)), a)), implies(not(a), implies(implies(a, a), implies(implies(not(a), a), a)))), implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))))), true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(not(a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 4 (condensed_detachment) }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(a), implies(not(not(a)), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.81    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(is_a_theorem(implies(not(not(a)), not(not(a)))), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.81  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.82  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true, ifeq(is_a_theorem(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.82  = { by axiom 2 (cn_19) }
% 98.29/12.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.82  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.82    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.83  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.83  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(not(implies(implies(T, implies(U, not(not(a)))), not(not(a)))), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(not(implies(implies(T, implies(U, not(not(a)))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.83  = { by axiom 3 (cn_37) }
% 98.29/12.83    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(not(implies(implies(T, implies(U, not(not(a)))), not(not(a)))), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true), true), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.84  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(not(implies(implies(T, implies(U, not(not(a)))), not(not(a)))), implies(not(not(a)), not(not(a))))), implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))))), true, is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.84  = { by axiom 5 (cn_60) }
% 98.29/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.84  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.84  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.84    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 2 (cn_19) R->L }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), not(not(a))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(implies(implies(implies(U, not(not(a))), not(not(a))), implies(not(not(a)), not(not(a)))), implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 4 (condensed_detachment) }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true, ifeq(true, true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 2 (cn_19) R->L }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a)))), implies(not(not(a)), not(not(a))))), true, ifeq(is_a_theorem(implies(implies(implies(T, implies(U, not(not(a)))), not(not(a))), implies(implies(U, not(not(a))), not(not(a))))), true, is_a_theorem(implies(not(not(a)), not(not(a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 4 (condensed_detachment) }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.85  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.85    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.86  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))))), true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.86  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.86  = { by axiom 5 (cn_60) R->L }
% 98.29/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(not(not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))))), true, is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.86  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.86    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(not(not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.87  = { by axiom 3 (cn_37) R->L }
% 98.29/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(not(not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(not(not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, is_a_theorem(implies(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.87  = { by axiom 4 (condensed_detachment) }
% 98.29/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.87  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.87  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.87    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.87  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(S, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(S, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 2 (cn_19) }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(S, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(S, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 2 (cn_19) }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.88  = { by axiom 2 (cn_19) R->L }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), a), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.89  = { by axiom 4 (condensed_detachment) }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.89  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.89  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.89  = { by axiom 4 (condensed_detachment) R->L }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.89  = { by axiom 3 (cn_37) }
% 98.29/12.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.90  = { by axiom 1 (ifeq_axiom) }
% 98.29/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.90  = { by axiom 1 (ifeq_axiom) R->L }
% 98.29/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 98.29/12.90  = { by axiom 2 (cn_19) R->L }
% 99.07/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.90  = { by axiom 1 (ifeq_axiom) R->L }
% 99.07/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.90  = { by axiom 2 (cn_19) R->L }
% 99.07/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(X2, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(X2, implies(implies(implies(Z, W), V), implies(W, V))), implies(not(a), implies(not(not(a)), a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(a), implies(not(not(a)), a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.90  = { by axiom 4 (condensed_detachment) }
% 99.07/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.90  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))))), true, ifeq(is_a_theorem(implies(not(not(a)), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true, is_a_theorem(implies(implies(not(not(a)), not(not(a))), implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 4 (condensed_detachment) }
% 99.07/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true, ifeq(true, true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 2 (cn_19) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z, W), V), implies(W, V)), implies(not(a), implies(not(not(a)), a)))), true, ifeq(is_a_theorem(implies(implies(implies(Z, W), V), implies(W, V))), true, is_a_theorem(implies(not(a), implies(not(not(a)), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 4 (condensed_detachment) }
% 99.07/12.91    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 4 (condensed_detachment) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Y2, implies(a, a)), implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(a, a)), implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 2 (cn_19) }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Y2, implies(a, a)), implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(Y2, implies(a, a)), implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 2 (cn_19) }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a))), implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(implies(a, a), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(a, implies(implies(not(a), a), a)), implies(implies(a, a), implies(implies(not(a), a), a)))), true), true), true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 4 (condensed_detachment) }
% 99.07/12.91    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.91    ifeq(ifeq(is_a_theorem(implies(a, implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 2 (cn_19) R->L }
% 99.07/12.91    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(Z2, implies(not(a), a)), a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(a, implies(implies(not(a), a), a))), true), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.91  = { by axiom 1 (ifeq_axiom) R->L }
% 99.07/12.92    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(not(a), a)), a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(a, implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.92  = { by axiom 2 (cn_19) R->L }
% 99.07/12.92    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(Z2, implies(not(a), a)), a), implies(implies(not(a), a), a)), implies(a, implies(implies(not(a), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(Z2, implies(not(a), a)), a), implies(implies(not(a), a), a))), true, is_a_theorem(implies(a, implies(implies(not(a), a), a))), true), true), true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.92  = { by axiom 4 (condensed_detachment) }
% 99.07/12.92    ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.92  = { by axiom 1 (ifeq_axiom) }
% 99.07/12.92    ifeq(is_a_theorem(implies(implies(a, a), implies(implies(not(a), a), a))), true, ifeq(is_a_theorem(implies(a, a)), true, is_a_theorem(implies(implies(not(a), a), a)), true), true)
% 99.07/12.92  = { by axiom 4 (condensed_detachment) }
% 99.07/12.92    true
% 99.07/12.92  % SZS output end Proof
% 99.07/12.92  
% 99.07/12.92  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------