Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n014.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 11:48:56 AM UTC 2026

% Result   : Unsatisfiable 54.29s 7.30s
% Output   : Proof 61.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n014.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 27 15:19:45 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.29/7.30  Command-line arguments: --no-flatten-goal
% 54.29/7.30  
% 54.29/7.30  % SZS status Unsatisfiable
% 54.29/7.30  
% 58.27/7.84  % SZS output start Proof
% 58.27/7.84  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 58.27/7.84  Axiom 2 (cn_3): is_a_theorem(implies(X, implies(not(X), Y))) = true.
% 58.27/7.84  Axiom 3 (cn_2): is_a_theorem(implies(implies(not(X), X), X)) = true.
% 58.27/7.84  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.
% 58.27/7.86  Axiom 5 (cn_1): is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z)))) = true.
% 58.27/7.86  
% 58.27/7.86  Goal 1 (prove_cn_49): is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))) = true.
% 58.27/7.86  Proof:
% 58.27/7.86    is_a_theorem(implies(implies(not(a), not(b)), implies(b, a)))
% 58.27/7.86  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.86    ifeq(true, true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 4 (condensed_detachment) R->L }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), a), implies(b, a))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 5 (cn_1) R->L }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), a)), implies(implies(implies(not(b), a), a), implies(b, a)))), true, is_a_theorem(implies(implies(implies(not(b), a), a), implies(b, a))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), a)), implies(implies(implies(not(b), a), a), implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 2 (cn_3) R->L }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(ifeq(is_a_theorem(implies(implies(b, implies(not(b), a)), implies(implies(implies(not(b), a), a), implies(b, a)))), true, ifeq(is_a_theorem(implies(b, implies(not(b), a))), true, is_a_theorem(implies(implies(implies(not(b), a), a), implies(b, a))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 4 (condensed_detachment) }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 1 (ifeq_axiom) }
% 58.27/7.86    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.86    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.86  = { by axiom 4 (condensed_detachment) R->L }
% 58.27/7.87    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.87  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.87  = { by axiom 5 (cn_1) R->L }
% 58.27/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.87  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.87  = { by axiom 5 (cn_1) R->L }
% 58.27/7.87    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a))), implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.88  = { by axiom 4 (condensed_detachment) }
% 58.27/7.88    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.88  = { by axiom 1 (ifeq_axiom) }
% 58.27/7.88    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.88  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.88    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.88  = { by axiom 4 (condensed_detachment) R->L }
% 58.27/7.88    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.88  = { by axiom 2 (cn_3) }
% 58.27/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.89  = { by axiom 1 (ifeq_axiom) }
% 58.27/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.89  = { by axiom 1 (ifeq_axiom) R->L }
% 58.27/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.89  = { by axiom 4 (condensed_detachment) R->L }
% 58.27/7.89    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.90  = { by axiom 5 (cn_1) }
% 58.27/7.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 58.27/7.90  = { by axiom 1 (ifeq_axiom) }
% 58.27/7.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.90  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/7.90    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.91  = { by axiom 4 (condensed_detachment) R->L }
% 59.02/7.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a)))), implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.91  = { by axiom 5 (cn_1) }
% 59.02/7.91    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.92  = { by axiom 1 (ifeq_axiom) }
% 59.02/7.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.92  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/7.92    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.93  = { by axiom 3 (cn_2) R->L }
% 59.02/7.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.93  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/7.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.93  = { by axiom 2 (cn_3) R->L }
% 59.02/7.93    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), a), a), implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(not(a), a), a)), true, is_a_theorem(implies(not(implies(implies(not(a), a), a)), not(not(implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.94  = { by axiom 4 (condensed_detachment) }
% 59.02/7.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.94  = { by axiom 1 (ifeq_axiom) }
% 59.02/7.94    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.95  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/7.95    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.95  = { by axiom 4 (condensed_detachment) R->L }
% 59.02/7.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a))), implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))))), true, ifeq(is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.96  = { by axiom 2 (cn_3) }
% 59.02/7.96    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a))), implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.96  = { by axiom 1 (ifeq_axiom) }
% 59.02/7.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a))), implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))))), true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.97  = { by axiom 5 (cn_1) }
% 59.02/7.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.97  = { by axiom 1 (ifeq_axiom) }
% 59.02/7.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a))))), true, ifeq(is_a_theorem(implies(implies(not(not(implies(implies(not(b), a), a))), implies(implies(not(a), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true, is_a_theorem(implies(not(implies(implies(not(b), a), a)), implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.97  = { by axiom 4 (condensed_detachment) }
% 59.02/7.97    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.98  = { by axiom 1 (ifeq_axiom) }
% 59.02/7.98    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.98  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/7.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/7.99  = { by axiom 4 (condensed_detachment) R->L }
% 59.02/7.99    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.00  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/8.01    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.01  = { by axiom 5 (cn_1) R->L }
% 59.02/8.02    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.02  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/8.03    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.03  = { by axiom 5 (cn_1) R->L }
% 59.02/8.04    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.04  = { by axiom 4 (condensed_detachment) }
% 59.02/8.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.05  = { by axiom 1 (ifeq_axiom) }
% 59.02/8.05    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.06  = { by axiom 1 (ifeq_axiom) R->L }
% 59.02/8.06    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 59.02/8.07  = { by axiom 4 (condensed_detachment) R->L }
% 60.51/8.07    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.07  = { by axiom 3 (cn_2) }
% 60.51/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.08  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.08    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.09  = { by axiom 5 (cn_1) }
% 60.51/8.09    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.09  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.10  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.10    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.10  = { by axiom 5 (cn_1) R->L }
% 60.51/8.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.11  = { by axiom 4 (condensed_detachment) }
% 60.51/8.11    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.11  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.12  = { by axiom 4 (condensed_detachment) }
% 60.51/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.12  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.12  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.12    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.12  = { by axiom 4 (condensed_detachment) R->L }
% 60.51/8.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.13  = { by axiom 5 (cn_1) }
% 60.51/8.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.13  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.13  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.13    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 5 (cn_1) R->L }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a))))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 3 (cn_2) R->L }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(a), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 4 (condensed_detachment) }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(a), a), a)), implies(implies(not(a), a), a)), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(a), a), a), implies(implies(not(b), a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.14  = { by axiom 4 (condensed_detachment) }
% 60.51/8.14    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.15  = { by axiom 1 (ifeq_axiom) }
% 60.51/8.15    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.15  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.15    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.15  = { by axiom 4 (condensed_detachment) R->L }
% 60.51/8.15    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.15  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.15    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.16  = { by axiom 5 (cn_1) R->L }
% 60.51/8.16    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.16  = { by axiom 1 (ifeq_axiom) R->L }
% 60.51/8.16    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.16  = { by axiom 5 (cn_1) R->L }
% 60.51/8.16    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 60.51/8.16  = { by axiom 4 (condensed_detachment) }
% 60.51/8.17    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.17  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.17    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.17  = { by axiom 1 (ifeq_axiom) R->L }
% 61.34/8.17    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.17  = { by axiom 4 (condensed_detachment) R->L }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 3 (cn_2) }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a))))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 5 (cn_1) }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 1 (ifeq_axiom) R->L }
% 61.34/8.18    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.18  = { by axiom 5 (cn_1) R->L }
% 61.34/8.19    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a))), implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)))), true, is_a_theorem(implies(implies(implies(implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.19  = { by axiom 4 (condensed_detachment) }
% 61.34/8.19    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.19  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.19    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a))), implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(not(implies(implies(not(b), a), a)), implies(implies(not(b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), a), implies(b, a)), implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)))), true), true), true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.19  = { by axiom 4 (condensed_detachment) }
% 61.34/8.19    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.19  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.19    ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true)
% 61.34/8.19  = { by axiom 1 (ifeq_axiom) R->L }
% 61.34/8.19    ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 4 (condensed_detachment) R->L }
% 61.34/8.19    ifeq(ifeq(is_a_theorem(implies(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a))), implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a))))), true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 5 (cn_1) }
% 61.34/8.19    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.19    ifeq(ifeq(is_a_theorem(implies(implies(not(a), not(b)), implies(implies(not(b), a), implies(not(a), a)))), true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 5 (cn_1) }
% 61.34/8.19    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 1 (ifeq_axiom) }
% 61.34/8.19    ifeq(is_a_theorem(implies(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a)), implies(implies(not(a), not(b)), implies(b, a)))), true, ifeq(is_a_theorem(implies(implies(implies(not(b), a), implies(not(a), a)), implies(b, a))), true, is_a_theorem(implies(implies(not(a), not(b)), implies(b, a))), true), true)
% 61.34/8.19  = { by axiom 4 (condensed_detachment) }
% 61.34/8.19    true
% 61.34/8.19  % SZS output end Proof
% 61.34/8.19  
% 61.34/8.19  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------