Twee---2.7.UNS-Prf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n001.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 11:48:51 AM UTC 2026

% Result   : Unsatisfiable 72.21s 9.60s
% Output   : Proof 81.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.33  % Computer : n001.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8046.5625MB
% 0.09/0.33  % OS       : Linux 6.8.0-71-generic
% 0.09/0.33  % CPULimit : 300
% 0.09/0.33  % WCLimit  : 300
% 0.09/0.33  % DateTime : Sun Sep 27 15:23:45 UTC 2026
% 0.09/0.33  % CPUTime  : 
% 0.09/0.33  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.21/9.60  Command-line arguments: --flatten-regeneralise
% 72.21/9.60  
% 72.21/9.60  % SZS status Unsatisfiable
% 72.21/9.60  
% 78.53/10.32  % SZS output start Proof
% 78.53/10.32  Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 78.53/10.32  Axiom 2 (c0_2): is_a_theorem(implies(X, implies(Y, X))) = true.
% 78.53/10.32  Axiom 3 (c0_5): is_a_theorem(implies(implies(implies(X, falsehood), falsehood), X)) = true.
% 78.53/10.32  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.
% 78.53/10.34  Axiom 5 (c0_6): is_a_theorem(implies(implies(X, implies(Y, Z)), implies(implies(X, Y), implies(X, Z)))) = true.
% 78.53/10.34  
% 78.53/10.34  Goal 1 (prove_c0_3): is_a_theorem(implies(implies(implies(a, b), a), a)) = true.
% 78.53/10.34  Proof:
% 78.53/10.34    is_a_theorem(implies(implies(implies(a, b), a), a))
% 78.53/10.34  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.34    ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.34  = { by axiom 4 (condensed_detachment) R->L }
% 78.53/10.34    ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.35  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.35    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.35  = { by axiom 4 (condensed_detachment) R->L }
% 78.53/10.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.35  = { by axiom 5 (c0_6) }
% 78.53/10.35    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.35  = { by axiom 1 (ifeq_axiom) }
% 78.53/10.35    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.36  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.36    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.36  = { by axiom 4 (condensed_detachment) R->L }
% 78.53/10.36    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.37  = { by axiom 5 (c0_6) }
% 78.53/10.37    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.38  = { by axiom 1 (ifeq_axiom) }
% 78.53/10.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.38  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.38    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.38  = { by axiom 5 (c0_6) R->L }
% 78.53/10.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.39  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.39  = { by axiom 2 (c0_2) R->L }
% 78.53/10.39    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.40  = { by axiom 4 (condensed_detachment) }
% 78.53/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.40  = { by axiom 1 (ifeq_axiom) }
% 78.53/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.40  = { by axiom 1 (ifeq_axiom) R->L }
% 78.53/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.40  = { by axiom 2 (c0_2) R->L }
% 78.53/10.40    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 78.53/10.41  = { by axiom 4 (condensed_detachment) }
% 79.33/10.41    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.41  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.41    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.41  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.41    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.41  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.41    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.41  = { by axiom 2 (c0_2) }
% 79.33/10.41    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))))), true), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.41  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.42    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 2 (c0_2) }
% 79.33/10.42    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))))), true), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.42    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)))), implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))))), true, ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, implies(implies(implies(implies(a, b), a), a), falsehood))))), true, is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)))), true), true), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 4 (condensed_detachment) }
% 79.33/10.42    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.42    ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.42    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.42    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.42    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.42  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.42    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.43  = { by axiom 5 (c0_6) }
% 79.33/10.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.43  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.43  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.43    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.44  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.44  = { by axiom 5 (c0_6) }
% 79.33/10.44    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.44  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.45  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.45    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.45  = { by axiom 5 (c0_6) R->L }
% 79.33/10.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.46  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.46  = { by axiom 2 (c0_2) R->L }
% 79.33/10.46    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))))), true, ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.47  = { by axiom 4 (condensed_detachment) }
% 79.33/10.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.47  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.47  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.47    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.47  = { by axiom 2 (c0_2) R->L }
% 79.33/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(a, b), a), a)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.48  = { by axiom 4 (condensed_detachment) }
% 79.33/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.48  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.48  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.48  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.48    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(a, implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 2 (c0_2) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(ifeq(is_a_theorem(implies(a, implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 2 (c0_2) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 4 (condensed_detachment) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.49    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.49  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.50  = { by axiom 5 (c0_6) }
% 79.33/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.50  = { by axiom 1 (ifeq_axiom) }
% 79.33/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.50  = { by axiom 1 (ifeq_axiom) R->L }
% 79.33/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.50  = { by axiom 4 (condensed_detachment) R->L }
% 79.33/10.50    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 79.33/10.50  = { by axiom 5 (c0_6) }
% 80.11/10.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.51  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.51  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.51  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.51    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true, ifeq(is_a_theorem(implies(falsehood, implies(implies(b, falsehood), falsehood))), true, is_a_theorem(implies(falsehood, b)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.52  = { by axiom 2 (c0_2) }
% 80.11/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true, ifeq(true, true, is_a_theorem(implies(falsehood, b)), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.52  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.52  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.52  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(b, falsehood), falsehood), b), implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b)))), true, ifeq(is_a_theorem(implies(implies(implies(b, falsehood), falsehood), b)), true, is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.52  = { by axiom 2 (c0_2) }
% 80.11/10.52    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(b, falsehood), falsehood), b)), true, is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.53  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(b, falsehood), falsehood), b)), true, is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.53  = { by axiom 3 (c0_5) }
% 80.11/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.53  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.53  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.53  = { by axiom 5 (c0_6) R->L }
% 80.11/10.53    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b)), implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b)))), true, ifeq(is_a_theorem(implies(falsehood, implies(implies(implies(b, falsehood), falsehood), b))), true, is_a_theorem(implies(implies(falsehood, implies(implies(b, falsehood), falsehood)), implies(falsehood, b))), true), true), true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.54  = { by axiom 4 (condensed_detachment) }
% 80.11/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(falsehood, b)), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.54  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(falsehood, b)), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.54  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(falsehood, b)), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.54  = { by axiom 2 (c0_2) R->L }
% 80.11/10.54    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(falsehood, b), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b)))), true, ifeq(is_a_theorem(implies(falsehood, b)), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(falsehood, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.54  = { by axiom 4 (condensed_detachment) }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 2 (c0_2) R->L }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 4 (condensed_detachment) }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.55    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.55  = { by axiom 2 (c0_2) }
% 80.11/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.56  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.56  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.56  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.56    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.57  = { by axiom 2 (c0_2) }
% 80.11/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.57  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.57  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.57    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.58  = { by axiom 4 (condensed_detachment) R->L }
% 80.11/10.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.58  = { by axiom 2 (c0_2) }
% 80.11/10.58    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.59  = { by axiom 1 (ifeq_axiom) }
% 80.11/10.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.59  = { by axiom 1 (ifeq_axiom) R->L }
% 80.11/10.59    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.60  = { by axiom 5 (c0_6) R->L }
% 80.11/10.60    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(X, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.11/10.60  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.60    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(X, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.61  = { by axiom 2 (c0_2) R->L }
% 80.91/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(X, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(X, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(X, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.61  = { by axiom 4 (condensed_detachment) }
% 80.91/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.61  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.61    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.62  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.62  = { by axiom 5 (c0_6) R->L }
% 80.91/10.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.62  = { by axiom 4 (condensed_detachment) }
% 80.91/10.62    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 5 (c0_6) R->L }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 4 (condensed_detachment) }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), a), implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true), true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 4 (condensed_detachment) }
% 80.91/10.63    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.63    ifeq(ifeq(ifeq(is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.63    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 5 (c0_6) R->L }
% 80.91/10.63    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b)), implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b)))), true, ifeq(is_a_theorem(implies(a, implies(implies(implies(implies(implies(a, b), a), a), falsehood), b))), true, is_a_theorem(implies(implies(a, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(a, b))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.63  = { by axiom 4 (condensed_detachment) }
% 80.91/10.63    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.64  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.64    ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true)
% 80.91/10.64  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.64    ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.64    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.64    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.64    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 2 (c0_2) }
% 80.91/10.64    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.64    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 3 (c0_5) }
% 80.91/10.64    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.64  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.65    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.65    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 5 (c0_6) R->L }
% 80.91/10.65    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 4 (condensed_detachment) }
% 80.91/10.65    ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.65    ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.65    ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.65    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 5 (c0_6) }
% 80.91/10.65    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.65  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.65    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 2 (c0_2) }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.66  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.66    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)), implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.67  = { by axiom 2 (c0_2) }
% 80.91/10.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.67  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.67    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.67  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.68  = { by axiom 4 (condensed_detachment) R->L }
% 80.91/10.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.68  = { by axiom 2 (c0_2) }
% 80.91/10.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.68  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.68    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.69  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.69  = { by axiom 5 (c0_6) R->L }
% 80.91/10.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(Y, implies(implies(a, b), a)), implies(implies(a, b), a))), implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a))))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.69  = { by axiom 1 (ifeq_axiom) R->L }
% 80.91/10.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(Y, implies(implies(a, b), a)), implies(implies(a, b), a))), implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.69  = { by axiom 2 (c0_2) R->L }
% 80.91/10.69    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(Y, implies(implies(a, b), a)), implies(implies(a, b), a))), implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a))))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(Y, implies(implies(a, b), a)), implies(implies(a, b), a)))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(Y, implies(implies(a, b), a))), implies(implies(implies(a, b), a), implies(implies(a, b), a)))), true), true), true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.70  = { by axiom 4 (condensed_detachment) }
% 80.91/10.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 80.91/10.70  = { by axiom 1 (ifeq_axiom) }
% 80.91/10.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.70  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.70  = { by axiom 5 (c0_6) R->L }
% 81.67/10.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(a, b), a), implies(implies(a, b), a)), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true, ifeq(is_a_theorem(implies(implies(implies(a, b), a), implies(implies(a, b), a))), true, is_a_theorem(implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.70  = { by axiom 4 (condensed_detachment) }
% 81.67/10.70    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 5 (c0_6) R->L }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a))), implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(implies(a, b), a), implies(a, b)), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), implies(a, b))), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 4 (condensed_detachment) }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 2 (c0_2) R->L }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(a, b), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a))))), true, ifeq(is_a_theorem(implies(implies(a, b), implies(implies(implies(a, b), a), a))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(a, b), implies(implies(implies(a, b), a), a)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.71  = { by axiom 4 (condensed_detachment) }
% 81.67/10.71    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.72    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.72    ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 4 (condensed_detachment) R->L }
% 81.67/10.72    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 5 (c0_6) }
% 81.67/10.72    ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.72    ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.72  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.72    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.73  = { by axiom 4 (condensed_detachment) R->L }
% 81.67/10.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.73  = { by axiom 5 (c0_6) }
% 81.67/10.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.73  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.73    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.74  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.74  = { by axiom 4 (condensed_detachment) R->L }
% 81.67/10.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.74  = { by axiom 2 (c0_2) }
% 81.67/10.74    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.75  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood)), implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.75  = { by axiom 5 (c0_6) }
% 81.67/10.75    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.75  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.76  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.76  = { by axiom 2 (c0_2) R->L }
% 81.67/10.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood))), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(Z, implies(implies(implies(implies(a, b), a), a), falsehood)))), true, is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(implies(a, b), a), a), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.76  = { by axiom 4 (condensed_detachment) }
% 81.67/10.76    ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.76  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 1 (ifeq_axiom) R->L }
% 81.67/10.77    ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 2 (c0_2) R->L }
% 81.67/10.77    ifeq(ifeq(ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 4 (condensed_detachment) }
% 81.67/10.77    ifeq(ifeq(ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.77    ifeq(ifeq(ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a))), implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood)))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(implies(implies(a, b), a), a)))), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(implies(implies(a, b), a), a), falsehood), falsehood))), true), true), true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 4 (condensed_detachment) }
% 81.67/10.77    ifeq(ifeq(true, true, is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 1 (ifeq_axiom) }
% 81.67/10.77    ifeq(is_a_theorem(implies(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b)), implies(implies(implies(a, b), a), a))), true, ifeq(is_a_theorem(implies(implies(implies(implies(implies(a, b), a), a), falsehood), implies(a, b))), true, is_a_theorem(implies(implies(implies(a, b), a), a)), true), true)
% 81.67/10.77  = { by axiom 4 (condensed_detachment) }
% 81.67/10.77    true
% 81.67/10.77  % SZS output end Proof
% 81.67/10.77  
% 81.67/10.77  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------